Recall that the permutation is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array) and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).

A sequence a is a subsegment of a sequence b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. We will denote the subsegments as [l, r], where l, r are two integers with 1 ≤ l ≤ r ≤ n. This indicates the subsegment where l-1 elements from the beginning and n-r elements from the end are deleted from the sequence.

For a permutation p_1, p_2, …, p_n, we define a framed segment as a subsegment [l,r] where max\\{p_l, p_{l+1}, ..., p_r\} - min\\{p_l, p_{l+1}, ..., p_r\} = r - l. For example, for the permutation (6, 7, 1, 8, 5, 3, 2, 4) some of its framed segments are: [1, 2], [5, 8], [6, 7], [3, 3], [8, 8]. In particular, a subsegment [i,i] is always a framed segments for any i between 1 and n, inclusive.

We define the happiness of a permutation p as the number of pairs (l, r) such that 1 ≤ l ≤ r ≤ n, and [l, r] is a framed segment. For example, the permutation [3, 1, 2] has happiness 5: all segments except [1, 2] are framed segments.

Given integers n and m, Jongwon wants to compute the sum of happiness for all permutations of length n, modulo the prime number m. Note that there exist n! (factorial of n) different permutations of length n.

Input

The only line contains two integers n and m (1 ≤ n ≤ 250 000, 10^8 ≤ m ≤ 10^9, m is prime).

Output

Print r (0 ≤ r < m), the sum of happiness for all permutations of length n, modulo a prime number m.

Examples

Input


1 993244853


Output


1


Input


2 993244853


Output


6


Input


3 993244853


Output


32


Input


2019 993244853


Output


923958830


Input


2020 437122297


Output


265955509

Note

For sample input n=3, let's consider all permutations of length 3:

  * [1, 2, 3], all subsegments are framed segment. Happiness is 6. 
  * [1, 3, 2], all subsegments except [1, 2] are framed segment. Happiness is 5. 
  * [2, 1, 3], all subsegments except [2, 3] are framed segment. Happiness is 5. 
  * [2, 3, 1], all subsegments except [2, 3] are framed segment. Happiness is 5. 
  * [3, 1, 2], all subsegments except [1, 2] are framed segment. Happiness is 5. 
  * [3, 2, 1], all subsegments are framed segment. Happiness is 6. 



Thus, the sum of happiness is 6+5+5+5+5+6 = 32.

import java.io.*;
import java.util.*;
import java.util.function.Predicate;
import java.util.stream.Collectors;

import static java.lang.Math.*;
import static java.lang.String.format;

public class Main {
    public static void main(String[] args) {
        solve();
    }
    final static int INF= Integer.MAX_VALUE>>2;
    final static int MOD = 1_000_000_007;
    final static int[] dx4 = { 0, 1, 0, -1 };
    final static int[] dy4 = { 1, 0, -1, 0 };
    final static int[] dx9 = {-1, -1, -1,  0,  0, 0, 1, 1,1};
    final static int[] dy9 = {-1, 0, 1, -1, 0, 1, -1, 0,1};
    final static Runnable me=()->{};
    public static void solve(){
        //TODO:Solve problem like ***
        final Scanner sc = new Scanner();
        final int n = sc.nextInt();
        final long m = sc.nextLong();
        final long[] kai = new long[n + 1];
        kai[0]=1;
        kai[1]=1;
        for (int i = 2; i < kai.length; i++) {
            kai[i] = i * kai[i - 1];
            kai[i] %= m;
        }
        long ans=0;
        for (int len = 1; len <= n; len++) {
            long anss = kai[n - len + 1] * kai[len];
            anss%=m;
            anss *= (n - len + 1);
            anss%=m;
            ans+=anss;
            ans %= m;
        }
        put(ans);


    }
    static class Encoder {
        final int m;

        public Encoder(int m) {
            this.m = m;
        }
        public int encode(int x,int y){
            assert y<m;
            return x * m + y;
        }
        public int decodeX(int z){
            return z / m;
        }
        public int decodeY(int z){
            return z % m;
        }
    }

    static class Accepter<T>{
        private T val;
        private final Predicate p;
        public Accepter(T defaultValue,Predicate p){
            this.val=defaultValue;
            this.p=p;
        }

        /**
         * @return accepted newval?
         */
        public boolean replace(T newVal){
            if(p.test(newVal)){
                this.val=newVal;
                return true;
            }
            return false;
        }
    }
    //runWhenEAで使う
    private static Runnable func(Object... objects){
        try{
            assert false;
            return me;
        }catch(AssertionError e){
            return ()->{put(objects);};
        }
    }
    private static void print(Object... objects){
        if(objects.length==1){
            System.out.print(objects[0]);
        }else{
            System.out.print(Arrays.toString(objects));
        }
    }
    private static void put(Object... objects) {
        print(objects);
        put();
    }
    private static void put(){
        System.out.println();
    }


    private static void runWhenEA(Runnable runnable){
        try{
            assert false;
        }catch(AssertionError e){
            PrintStream ps=System.out;
            PrintStream pse=System.err;
            System.setOut(pse);
            runnable.run();
            System.setOut(ps);
        }
    }
    private static void putM(String name,char[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    private static void putM(String name,int[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    private static void putM(String name,long[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    private static void putM(String name,boolean[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    final static private class Scanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;

        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (hasNextByte())
                return buffer[ptr++];
            else
                return -1;
        }

        private boolean isPrintableChar(int c) {
            return 33 <= c && c <= 126;
        }

        public boolean hasNext() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr]))
                ptr++;
            return hasNextByte();
        }

        public String next() {
            if (!hasNext())
                throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public long nextLong() {
            if (!hasNext())
                throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while (true) {
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                } else if (b == -1 || !isPrintableChar(b)) {
                    return minus ? -n : n;
                } else {
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }

        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
                throw new NumberFormatException();
            return (int) nl;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
    static private class FixedIntPair {
        final public int x, y;
        final static public FixedIntPair ZEROS=new FixedIntPair(0,0);
        FixedIntPair(int x, int y) {
            this.x = x;
            this.y = y;
        }
        @Override
        public String toString() {
            return format(FixedIntPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class FixedLongPair {
        final public long x, y;
        final static public FixedLongPair ZEROS=new FixedLongPair(0,0);
        FixedLongPair(long x, long y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int hashCode() {
            return (int)x+(int)y;
        }

        @Override
        public boolean equals(Object obj) {
            if(obj==null)return false;
            if(!(obj instanceof FixedLongPair)) return false;
            FixedLongPair pair=(FixedLongPair)obj;
            return this.x==pair.x&&this.y==pair.y;
        }

        @Override
        public String toString() {
            return format(FixedLongPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class Binary{
        public static String toZeroPadding(int i){
            return format("%"+Integer.toBinaryString(-1).length()+"s",Integer.toBinaryString(i)).replace(' ','0');
        }
        public static String toZeroPadding(long i){
            return format("%"+Long.toBinaryString(-1).length()+"s",Long.toBinaryString(i)).replace(' ','0');
        }
    }
    public static class BinaryIndexedTree {
        final int n;
        final long[] array;
        BinaryIndexedTree(long[] array){
            this.n=array.length;
            this.array=new long[n];
            for(int i=0;i<array.length;i++){
                add(i,array[i]);
            }
        }
        BinaryIndexedTree(int[] array){
            this.n=array.length;
            this.array=new long[n];
            for(int i=0;i<array.length;i++){
                add(i,array[i]);
            }
        }
        public void add(int index,long val){
            for(;index<n;index|=index+1){
                array[index]+=val;
            }
        }
        public long sum(int index){
            long result=0;
            for(;index>=0;index=(index&(index+1))-1){
                result+=array[index];
            }
            return result;
        }

        /**
         *
         * @param array arrayが1～nの順列になっていないならば定義されない
         * @return 転倒数
         */
        public static int inv(int[] array){
            int[] a=new int[array.length];
            BinaryIndexedTree bit=new BinaryIndexedTree(a);
            bit.add(array[0]-1,1);
            int result=0;
            for(int i=1;i<array.length;i++){
                System.out.println(bit);
                result+=i-bit.sum(array[i]-1);
                bit.add(array[i]-1,1);
            }
            return result;
        }

        @Override
        public String toString() {
            long[] array=new long[n];
            for(int i=0;i<n;i++){
                array[i]=sum(i);
            }
            String result="";
            result+="ruiseki:"+ Arrays.toString(array)+"\n";
            array[0]=sum(0);
            for(int i=1;i<n;i++){
                array[i]=sum(i)-sum(i-1);
            }
            result+="source::"+Arrays.toString(array);
            return result;
        }
    }

    final static private class Util {
        static long gcd(long a,long b){
            a= abs(a);
            b= abs(b);
            if(a<b){
                long tmp=a;
                a=b;
                b=tmp;
            }
            while(b!=0){
                long r=a%b;
                a=b;
                b=r;
            }
            return a;
        }
        static int gcd(int a,int b){
            a= abs(a);
            b= abs(b);
            if(a<b){
                int tmp=a;
                a=b;
                b=tmp;
            }
            while(b!=0){
                int r=a%b;
                a=b;
                b=r;
            }
            return a;
        }
        static long lcm(long a,long b){
            long gcd=gcd(a,b);
            long result=b/gcd;
            return a*result;
        }
        static boolean isValidCell(int i,int j,int h,int w){
            return i>=0&&i<h&&j>=0&&j<w;
        }
    }
}































































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 */
