In some game by Playrix it takes t minutes for an oven to bake k carrot cakes, all cakes are ready at the same moment t minutes after they started baking. Arkady needs at least n cakes to complete a task, but he currently don't have any. However, he has infinitely many ingredients and one oven. Moreover, Arkady can build one more similar oven to make the process faster, it would take d minutes to build the oven. While the new oven is being built, only old one can bake cakes, after the new oven is built, both ovens bake simultaneously. Arkady can't build more than one oven.

Determine if it is reasonable to build the second oven, i.e. will it decrease the minimum time needed to get n cakes or not. If the time needed with the second oven is the same as with one oven, then it is unreasonable.

Input

The only line contains four integers n, t, k, d (1 ≤ n, t, k, d ≤ 1 000) — the number of cakes needed, the time needed for one oven to bake k cakes, the number of cakes baked at the same time, the time needed to build the second oven. 

Output

If it is reasonable to build the second oven, print "YES". Otherwise print "NO".

Examples

Input

8 6 4 5


Output

YES


Input

8 6 4 6


Output

NO


Input

10 3 11 4


Output

NO


Input

4 2 1 4


Output

YES

Note

In the first example it is possible to get 8 cakes in 12 minutes using one oven. The second oven can be built in 5 minutes, so after 6 minutes the first oven bakes 4 cakes, the second oven bakes 4 more ovens after 11 minutes. Thus, it is reasonable to build the second oven. 

In the second example it doesn't matter whether we build the second oven or not, thus it takes 12 minutes to bake 8 cakes in both cases. Thus, it is unreasonable to build the second oven.

In the third example the first oven bakes 11 cakes in 3 minutes, that is more than needed 10. It is unreasonable to build the second oven, because its building takes more time that baking the needed number of cakes using the only oven.
		import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.ObjectInputStream.GetField;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Objects;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
	
		
		
		
		
			public class Q1 {
				
				static long MOD = 1000000007;
				static boolean b[], b1[], check;
				static ArrayList<Integer>[] amp, pa;
				static ArrayList<Pair>[] amp1;
				static ArrayList<Pair>[][] damp;
				static int left[],s[],right[],end[],sum[],dist[],cnt[],start[],color[],parent[],prime[],size[];
				static long ans = 0,k;
				static int p = 0;
				static FasterScanner sc = new FasterScanner(System.in);
				static Queue<Integer> q = new LinkedList<>();
				static PriorityQueue<Pair> pq;
				static BufferedWriter log;
				static HashSet<Pair> hs;
				static HashMap<Pair,Integer> hm;
				static PriorityQueue<Integer> pri[];
				static ArrayList<Integer>[] level;
				static Stack<Integer> st;
				static boolean boo[][];
				static Pair prr[];
				static long parent1[],parent2[],size1[],size2[],arr1[],SUM[],lev[], fibo[];
				static int  ver[][];
				public static void main(String[] args) throws Exception {
			    	/*new Thread(null, new Runnable() {
						public void run() {
							try {
		
						} catch (Exception e) {
								System.out.println(e);
							}
						}
					}, "1", 1 << 26).start();*/
					soln();
				}
				static int dp[];
				static int N,K,T;
				static int time;
				static int cost[][];
				static boolean b11[];
				static HashMap<Integer,Integer> h = new HashMap<>();
				static HashSet<Pair> chec;
				static long ans1;		static long ans2;
				static int BLOCK, MAX = 200000;
				static double pi = Math.PI;
				static int Arr[], Brr[], pow[],  M;
				static long fact[] = new long[100000+1];
				static double arr[][];
				public static void soln() throws IOException {
					//FasterScanner in = new FasterScanner(new FileInputStream("C:\\Users\\Admin\\Desktop\\QAL.txt"));
					//PrintWriter out = new PrintWriter("C:\\Users\\Admin\\Desktop\\A1.txt");
					//Scanner in = new Scanner(System.in);//new FileInputStream("C:\\Users\\Admin\\Desktop\\QBS.txt"));
					log = new BufferedWriter(new OutputStreamWriter(System.out));
					int n = sc.nextInt(), t = sc.nextInt(), k = sc.nextInt(), d = sc.nextInt();
					int t1 = (int) (Math.ceil((double)n/k)*t);
					int cakes = n;
					int time = 0;
					while(cakes>0){
						if(time>d){
							if((time-d)%t==0){
								cakes-=k;
							}
						}
						if(time>0 && time%t==0){
							cakes-=k;
						}
						if(cakes<=0) break;
						time++;
					}
					//int x = Math.max(n - (g/t)*k,0); 
					//int y = Math.min(n - g/t + k,n);
					//int t2 = Math.max(d,g) + (int) (Math.ceil((double)(x)/(2.0*k)))*t;
					//int t3 = Math.max(g - t,d) + (int) (Math.ceil((double)(y)/(2.0*k)))*t;
					//int t11 = Math.min(t2, t3);
					//System.out.println(t11+" "+t2+" "+t3);
					//System.out.println(time);
					if(time<t1){
						System.out.println("YES");
					}
					else System.out.println("NO");
					//out.close();
					log.close();
				}
				static int countCommMult(int arr[], int l, int h){
					int ans = 0;
					int n = arr.length;
					long lcm = arr[0];
					for(int i = 1; i<n;i++){
						lcm = (lcm*(arr[i]))/gcd(lcm,arr[i]);
						if(lcm>2000000000) return 0;
					}
					ans = (int) (h/lcm-l/lcm);
					return ans;
				}
				static long nCr(int n, int r){
					if(n<r) return 0;
					else return (((fact[n]*modInverse(fact[r], MOD))%MOD)*modInverse(fact[n-r], MOD))%MOD;
				}
				static void dfs1(int x, int p){
					arr1[x] += lev[x];
					for(int v:amp[x]){
						if(v!=p){
							dfs1(v,x);
						}
					}
				}
				static void bfs(){
					q = new LinkedList<>();
					q.add(0);
					while(!q.isEmpty()){
						int y = q.poll();
						b[y] = true;
						level[dist[y]].add(start[y]);
						for(int x:amp[y]){
							if(!b[x]){
								q.add(x);
								dist[x] = 1+dist[y];	
							}
						}
					}
				}
				static void dfs(int x, int p){
					start[x] = time++;
					for(int v:amp[x]){
						if(v!=p){
							dfs(v,x);
						}
					}
					end[x] = time;
				}
				public static class FenwickTree {
	
				    int[] array; // 1-indexed array, In this array We save cumulative information to perform efficient range queries and updates
	
				    public FenwickTree(int size) {
				        array = new int[size + 1];
				    }
				    public int rsq(int ind) {
				        assert ind > 0;
				        int sum = 0;
				        while (ind > 0) {
				            sum += array[ind];
				            //Extracting the portion up to the first significant one of the binary representation of 'ind' and decrementing ind by that number
				            ind -= ind & (-ind);
				        }
				        return sum;
				    }
				    public int rsq(int a, int b) {
				        assert b >= a && a > 0 && b > 0;
				        return rsq(b) - rsq(a - 1);
				    }
				    public void update(int ind, int value) {
				        assert ind > 0;
				        while (ind < array.length) {
				            array[ind] += value;
				            //Extracting the portion up to the first significant one of the binary representation of 'ind' and incrementing ind by that number
				            ind += ind & (-ind);
				        }
				    }
	
				    public int size() {
				        return array.length - 1;
				    }
				}
				static void bfs(int x){
					
				}
				static void dfs(int x){
					b[x] = true;
					if(amp[x].size()%2==1) p++;
					for(int p:amp[x]){
						if(!b[p]){
							dfs(p);
						}
					}
				}
				public static void seive(int n){
					b = new boolean[(n+1)];
					Arrays.fill(b, true);
					b[1] = true;
					for(int i = 2;i*i<=n;i++){
						if(b[i]){
							for(int p = 2*i;p<=n;p+=i){
								b[p] = false;
							}
						}
					}
					/*for(int i = 2;i<=n;i++){
						if(b[i]) prime[i] = i;
					}*/
				}
				
				static class Graph{
					int vertex;
					int weight;
					Graph(int v, int w){
						vertex = v;
						weight = w;
					}
				}
				static class Pair implements Comparable<Pair> {
					int u;
					int v;
					public Pair(){
						u = 0;
						v = 0;
					}
					public Pair(int u, int v) {
						this.u = u;
						this.v = v;
					}
					public int hashCode() {
						return Objects.hash();
					}
					public boolean equals(Object o) {
						Pair other = (Pair) o;
						return ((u == other.u && v == other.v));
					}
			 
					public int compareTo(Pair other) {
						//return Double.compare(ans, other.ans);
						return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(v,other.v));
					}
					
					public String toString() {
						return "[u=" + u + ", v=" + v + "]";
					}
				}
				
				public static void buildGraph(int n){
					for(int i =0;i<n;i++){
						int x = sc.nextInt()-1, y = sc.nextInt()-1;
						//hm.put(new Pair(x,y), i+1);
						amp[x].add(y);
						amp[y].add(x);
					}
				}
				
				
				public static int getParent(long x){
					while(parent[(int) x]!=x){
						parent[ (int) x] = parent[(int) parent[ (int) x]];
						x = parent[ (int) x];
					}
					return (int) x;
				}
				static long min(long a, long b, long c){
					if(a<b && a<c) return a;
					if(b<c) return b;
					return c;
				}
				/*
				
				static class Pair3{
					int x, y ,z;
					Pair3(int x, int y, int z){
						this.x = x;
						this.y = y;
						this.z = z;
					}
				}*/
				 static void KMPSearch(String pat, String txt)
				    {
				        int M = pat.length();
				        int N = txt.length();
				 
				        // create lps[] that will hold the longest
				        // prefix suffix values for pattern
				        int lps[] = new int[M];
				        int j = 0;  // index for pat[]
				 
				        // Preprocess the pattern (calculate lps[]
				        // array)
				        computeLPSArray(pat,M,lps);
				 
				        int i = 0;  // index for txt[]
				        while (i < N)
				        {
				            if (pat.charAt(j) == txt.charAt(i))
				            {
				                j++;
				                i++;
				            }
				            if (j == M)
				            {
				               // parent.add((i-j));
				                j = lps[j-1];
				            }
				 
				            // mismatch after j matches
				            else if (i < N && pat.charAt(j) != txt.charAt(i))
				            {
				                // Do not match lps[0..lps[j-1]] characters,
				                // they will match anyway
				                if (j != 0)
				                    j = lps[j-1];
				                else
				                    i = i+1;
				            }
				        }
				    }
				 static void computeLPSArray(String pat, int M, int lps[])
				    {
				        // length of the previous longest prefix suffix
				        int len = 0;
				        int i = 1;
				        lps[0] = 0;  // lps[0] is always 0
				 
				        // the loop calculates lps[i] for i = 1 to M-1
				        while (i < M)
				        {
				            if (pat.charAt(i) == pat.charAt(len))
				            {
				                len++;
				                lps[i] = len;
				                i++;
				            }
				            else  // (pat[i] != pat[len])
				            {
				                // This is tricky. Consider the example.
				                // AAACAAAA and i = 7. The idea is similar 
				                // to search step.
				                if (len != 0)
				                {
				                    len = lps[len-1];
				 
				                    // Also, note that we do not increment
				                    // i here
				                }
				                else  // if (len == 0)
				                {
				                    lps[i] = len;
				                    i++;
				                }
				            }
				        }
				    }
				private static void permutation(String prefix, String str) {
				    int n = str.length();
				    if (n == 0); //hs.add(prefix);
				    else {
				        for (int i = 0; i < n; i++)
				            permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n));
				    }
				}
				
				public static void buildTree(int n){
					int arr[] = sc.nextIntArray(n);
					for(int i = 0;i<n;i++){
						int x = arr[i]-1;
						amp[i+1].add(x);
						amp[x].add(i+1);
					}
				}
				
				static class SegmentTree {
					boolean st[];
					boolean lazy[];
		
					SegmentTree(int n) {
						int size = 4 * n;
						st = new boolean[size];
						Arrays.fill(st, true);
						lazy = new boolean[size];
						Arrays.fill(lazy, true);
						//build(0, n - 1, 1);
					}
					
					/*long[] build(int ss, int se, int si) {
						if (ss == se) {
							st[si][0] = 1;
							st[si][1] = 1;
							st[si][2] = 1;
							return st[si];
						}
						int mid = (ss + se) / 2;
						long a1[] = build(ss, mid, si * 2), a2[] = build(mid + 1, se,
								si * 2 + 1);
						long ans[] = new long[3];
						if (arr[mid] < arr[mid + 1]) {
							ans[1] = Math.max(a2[1], Math.max(a1[1], a1[2] + a2[0]));
							if (a1[1] == (mid - ss + 1))
								ans[0] = ans[1];
							else
								ans[0] = a1[0];
							if (a2[2] == (se - mid))
								ans[2] = ans[1];
							else
								ans[2] = a2[2];
						} else {
							ans[1] = Math.max(a1[1], a2[1]);
							ans[0] = a1[0];
							ans[2] = a2[2];
						}
						st[si] = ans;
						return st[si];
					}*/
		
					void update(int si, int ss, int se, int idx, long x) {
						if (ss == se) {
							//arr[idx] += val;
							st[si]=false;
						} 
						else {
							int mid = (ss + se) / 2;
							if(ss <= idx && idx <= mid)
					        {
					             update(2*si, ss, mid, idx, x);
					        }
					        else
					        { update(2*si+1, mid+1, se, idx, x);
					        }
							st[si] = st[2*si]|st[2*si+1];
						}
					}
					/*boolean get(int qs, int qe, int ss, int se, int si){
						if(qs>se || qe<ss) return 0;
						if (qs <= ss && qe >= se) {
							return st[si];
						}
						int mid = (ss+se)/2;
						return get(qs, qe, ss, mid, si * 2)+get(qs, qe, mid + 1, se, si * 2 + 1);
					}*/
					void updateRange(int node, int start, int end, int l, int r, boolean val)
					{
					    if(!lazy[node])
					    { 
					        // This node needs to be updated
					        st[node] = lazy[node];    // Update it
					        if(start != end)
					        {
					            lazy[node*2] = lazy[node];                  // Mark child as lazy
					            lazy[node*2+1] = lazy[node];                // Mark child as lazy
					        }
					        lazy[node] = true;                                  // Reset it
					    }
					    if(start > end || start > r || end < l)              // Current segment is not within range [l, r]
					        return;
					    if(start >= l && end <= r)
					    {
					        // Segment is fully within range
					        st[node] =  val;
					        if(start != end)
					        {
					            // Not leaf node
					            lazy[node*2] = val;
					            lazy[node*2+1] = val;
					        }
					        return;
					    }
					    int mid = (start + end) / 2;
					    updateRange(node*2, start, mid, l, r, val);        // Updating left child
					    updateRange(node*2 + 1, mid + 1, end, l, r, val);   // Updating right child
					    st[node] = st[node*2] | st[node*2+1];        // Updating root with max value 
					}
		
					boolean queryRange(int node, int start, int end, int l, int r)
					{
					    if(start > end || start > r || end < l)
					        return false;         // Out of range
					    if(!lazy[node])
					    {
					        // This node needs to be updated
					        st[node] = lazy[node];            // Update it
					        if(start != end)
					        {
					            lazy[node*2] = lazy[node];         // Mark child as lazy
					            lazy[node*2+1] = lazy[node];    // Mark child as lazy
					        }
					        lazy[node] = true;                 // Reset it
					    }
					    if(start >= l && end <= r)             // Current segment is totally within range [l, r]
					        return  st[node];
					    int mid = (start + end) / 2;
					    boolean p1 = queryRange(node*2, start, mid, l, r);         // Query left child
					    boolean b = queryRange(node*2 + 1, mid + 1, end, l, r); // Query right child
					    return (p1 | b);
					}
					void print() {
						for (int i = 0; i < st.length; i++) {
							System.out.print(st[i]+" ");
						}
						System.out.println();
					}
				}
				static int convert(int x){
					int cnt = 0;
					String str = Integer.toBinaryString(x);
					//System.out.println(str);
					for(int i = 0;i<str.length();i++){
						if(str.charAt(i)=='1'){
							cnt++;
						}
					}
					int ans = (int) Math.pow(3, 6-cnt);
					return ans;
				}
				static class Node2{
					Node2 left = null;
					Node2 right = null;
					Node2 parent = null;
					int data;
				}
				static class BinarySearchTree{
					Node2 root = null;
					int height = 0;
					int max = 0;
					int cnt = 1;
					ArrayList<Integer> parent = new ArrayList<>();
					HashMap<Integer, Integer> hm = new HashMap<>();
					public void insert(int x){
						Node2 n = new Node2();
						n.data = x;
						if(root==null){
							root = n;
						}
						else{
							Node2 temp = root,temb = null;
							while(temp!=null){
								temb = temp;
								if(x>temp.data) temp = temp.right;
								else temp = temp.left;
							}
							if(x>temb.data) temb.right = n;
							else temb.left = n;
							n.parent = temb;
							parent.add(temb.data);
						}
					}
					public Node2 getSomething(int x, int y, Node2 n){
						if(n.data==x || n.data==y) return n;
						else if(n.data>x && n.data<y) return n;
						else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
						else return getSomething(x,y,n.left);
					}
					public Node2 search(int x,Node2 n){
						if(x==n.data){
							max = Math.max(max, n.data);
							return n;
						}
						if(x>n.data){
							max = Math.max(max, n.data);
							return search(x,n.right);
						}
						else{
							max = Math.max(max, n.data);
							return search(x,n.left);
						}
					}
					public int getHeight(Node2 n){
						if(n==null) return 0;
						height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
						return height;
					}
				}
				static long findDiff(long[] arr, long[] brr, int m){
					int i = 0, j = 0;
					long fa = 1000000000000L;
					while(i<m && j<m){
						long x = arr[i]-brr[j];
						if(x>=0){
							if(x<fa) fa = x;
							j++;
						}
						else{
							if((-x)<fa) fa = -x;
							i++;
						}
					}
					return fa;
				}
				public static long max(long x, long y, long z){
					if(x>=y && x>=z) return x;
					if(y>=x && y>=z) return y;
					return z;
				}
				
				static long modInverse(long a, long mOD2){
				            return  power(a, mOD2-2, mOD2);
				}
				static long power(long x, long y, long m)
				{
				    if (y == 0)
				        return 1;
				    long p = power(x, y/2, m) % m;
				    p = (p * p) % m;
				 
				    return (y%2 == 0)? p : (x * p) % m;
				}
				static long d,x,y;
				public static void extendedEuclidian(long a, long b){
					if(b == 0) {
				        d = a;
				        x = 1;
				        y = 0;
				    }
				    else {
				        extendedEuclidian(b, a%b);
				        int temp = (int) x;
				        x = y;
				        y = temp - (a/b)*y;
				    }
				}
				
				public static long gcd(long n, long m){
					if(m!=0) return gcd(m,n%m);
					else return n;
				}
				
				static BufferedReader reader;
			    static StringTokenizer tokenizer;
			    static PrintWriter writer;
			
			
			   
			    static class FasterScanner {
		
					private final InputStream stream;
					private final byte[] buf = new byte[8192];
					private int curChar, snumChars;
					private SpaceCharFilter filter;
		
					public FasterScanner(InputStream stream) {
						this.stream = stream;
					}
		
					public int snext() {
						if (snumChars == -1)
							throw new InputMismatchException();
						if (curChar >= snumChars) {
							curChar = 0;
							try {
								snumChars = stream.read(buf);
							} catch (IOException e) {
								throw new InputMismatchException();
							}
							if (snumChars <= 0)
								return -1;
						}
						return buf[curChar++];
					}
		
					public int nextInt() {
						int c = snext();
						while (isSpaceChar(c)) {
							c = snext();
						}
						int sgn = 1;
						if (c == '-') {
							sgn = -1;
							c = snext();
						}
						int res = 0;
						do {
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = snext();
						} while (!isSpaceChar(c));
						return res * sgn;
					}
		
					public long nextLong() {
						int c = snext();
						while (isSpaceChar(c)) {
							c = snext();
						}
						int sgn = 1;
						if (c == '-') {
							sgn = -1;
							c = snext();
						}
						long res = 0;
						do {
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = snext();
						} while (!isSpaceChar(c));
						return res * sgn;
					}
		
					public int[] nextIntArray(int n) {
						int a[] = new int[n];
						for (int i = 0; i < n; i++) {
							a[i] = nextInt();
						}
						return a;
					}
		
					public long[] nextLongArray(int n) {
						long a[] = new long[n];
						for (int i = 0; i < n; i++) {
							a[i] = nextLong();
						}
						return a;
					}
			                
					public String readString() {
						int c = snext();
						while (isSpaceChar(c)) {
							c = snext();
						}
						StringBuilder res = new StringBuilder();
						do {
							res.appendCodePoint(c);
							c = snext();
						} while (!isSpaceChar(c));
						return res.toString();
					}
		
					public String nextLine() {
						int c = snext();
						while (isSpaceChar(c))
							c = snext();
						StringBuilder res = new StringBuilder();
						do {
							res.appendCodePoint(c);
							c = snext();
						} while (!isEndOfLine(c));
						return res.toString();
					}
		
					public boolean isSpaceChar(int c) {
						if (filter != null)
							return filter.isSpaceChar(c);
						return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
					}
		
					private boolean isEndOfLine(int c) {
						return c == '\n' || c == '\r' || c == -1;
					}
		
					public interface SpaceCharFilter {
						public boolean isSpaceChar(int ch);
					}
				}
			}  