To AmShZ, all arrays are equal, but some arrays are more-equal than others. Specifically, the arrays consisting of n elements from 1 to n that can be turned into permutations of numbers from 1 to n by adding a non-negative integer to each element.

Mashtali who wants to appear in every problem statement thinks that an array b consisting of k elements is compatible with a more-equal array a consisting of n elements if for each 1 ≤ i ≤ k we have 1 ≤ b_i ≤ n and also a_{b_1} = a_{b_2} = … = a_{b_k}.

Find the number of pairs of arrays a and b such that a is a more-equal array consisting of n elements and b is an array compatible with a consisting of k elements modulo 998244353.

Note that the elements of b are not necessarily distinct, same holds for a.

Input

The first line of input contains two integers n and k (1 ≤ n ≤ 10^9 , 1 ≤ k ≤ 10^5).

Output

Print a single integer — the answer to the problem modulo 998244353.

Examples

Input


1 1


Output


1


Input


2 2


Output


8


Input


5 4


Output


50400


Input


20 100


Output


807645526


Input


10000000 10000


Output


883232350

Note

There are eight possible pairs for the second example: 

  1. a = \{1, 1\}, b = \{1, 1\} 
  2. a = \{1, 1\}, b = \{1, 2\} 
  3. a = \{1, 1\}, b = \{2, 1\} 
  4. a = \{1, 1\}, b = \{2, 2\} 
  5. a = \{1, 2\}, b = \{1, 1\} 
  6. a = \{1, 2\}, b = \{2, 2\} 
  7. a = \{2, 1\}, b = \{1, 1\} 
  8. a = \{2, 1\}, b = \{2, 2\} 
#include<bits/stdc++.h>
#define For(i,a,b) for(register int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(register int i=(a);i>=(b);--i)
using namespace std;
inline int read()
{
    char c=getchar();int x=0;bool f=0;
    for(;!isdigit(c);c=getchar())f^=!(c^45);
    for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
    if(f)x=-x;return x;
}
 
#define mod 998244353
struct modint{
    int x;
    modint(int o=0){x=o;}
    modint &operator = (int o){return x=o,*this;}
    modint &operator +=(modint o){return x=x+o.x>=mod?x+o.x-mod:x+o.x,*this;}
    modint &operator -=(modint o){return x=x-o.x<0?x-o.x+mod:x-o.x,*this;}
    modint &operator *=(modint o){return x=1ll*x*o.x%mod,*this;}
    modint &operator ^=(int b){
        modint a=*this,c=1;
        for(;b;b>>=1,a*=a)if(b&1)c*=a;
        return x=c.x,*this;
    }
    modint &operator /=(modint o){return *this *=o^=mod-2;}
    modint &operator +=(int o){return x=x+o>=mod?x+o-mod:x+o,*this;}
    modint &operator -=(int o){return x=x-o<0?x-o+mod:x-o,*this;}
    modint &operator *=(int o){return x=1ll*x*o%mod,*this;}
    modint &operator /=(int o){return *this *= ((modint(o))^=mod-2);}
    template<class I>friend modint operator +(modint a,I b){return a+=b;}
    template<class I>friend modint operator -(modint a,I b){return a-=b;}
    template<class I>friend modint operator *(modint a,I b){return a*=b;}
    template<class I>friend modint operator /(modint a,I b){return a/=b;}
    friend modint operator ^(modint a,int b){return a^=b;}
    friend bool operator ==(modint a,int b){return a.x==b;}
    friend bool operator !=(modint a,int b){return a.x!=b;}
    bool operator ! () {return !x;}
    modint operator - () {return x?mod-x:0;}
};
inline modint qpow(modint a,int b){return a^b;}

#define maxn 800005
const modint G=3,Ginv=modint(1)/3;
struct poly{
    vector<modint>a;
    modint& operator [](int i){return a[i];}
    int size(){return a.size();}
    void resize(int n){a.resize(n);}
};
inline poly one(){poly a;a.a.push_back(1);return a;}
int rev[maxn];
inline int ext(int n){
	int k=0;
	while((1<<k)<n)++k;return k; 
}
inline void init(int k){
	int n=1<<k;
	For(i,0,n-1)rev[i]=(rev[i>>1]>>1)|((i&1)<<(k-1));
}
void ntt(poly&a,int k,int typ)
{
	int n=1<<k;
	For(i,0,n-1)if(i<rev[i])swap(a[i],a[rev[i]]); 
	for(int mid=1;mid<n;mid<<=1)
	{
		modint wn=(typ>0?G:Ginv)^((mod-1)/(mid<<1));
		for(int r=mid<<1,j=0;j<n;j+=r){
			modint w=1;
			for(int k=0;k<mid;++k,w=w*wn){
				modint x=a[j+k],y=w*a[j+k+mid];
				a[j+k]=x+y,a[j+k+mid]=x-y;
			}
		}
	}
	if(typ<0){
		modint inv=modint(1)/n;
		For(i,0,n-1)a[i]*=inv;
	}
}

poly operator *(poly a,poly b)
{
	int n=(int)a.size()+(int)b.size()-1,k=ext(n);
	a.resize(1<<k),b.resize(1<<k),init(k);
	ntt(a,k,1),ntt(b,k,1);
	For(i,0,(1<<k)-1)a[i]*=b[i];
	ntt(a,k,-1),a.resize(n);return a;
}

int n,k;
modint fac[maxn],ifac[maxn],iv[maxn];
inline modint sign(int x){return (x&1)?(mod-1):(1);}
poly f,g,s,a,b;
inline void get_s(int n){
	fac[0]=ifac[0]=1;
	For(i,1,n+n)
		fac[i]=fac[i-1]*i,
		iv[i]=modint(1)/i,
		ifac[i]=ifac[i-1]*iv[i];
	int sz=n+1;
	a.resize(sz),b.resize(sz);
	For(i,0,n)
		a[i]=sign(i)*ifac[i],
		b[i]=(modint(i)^n)*ifac[i];
	s=a*b; s.resize(n+1);
}

int main()
{
	n=read(),k=read();
	get_s(k);
	modint res=0,C=1;
	For(i,1,k){
		if(n-i+1==0)break;
		C*=(n-i+1),C/=i;
		res+=s[i]*fac[i]*C*qpow(n+1,n-i);
	}
	cout<<res.x;
    return 0;
}