Problem: Given is a string S consisting of `0` and `1`. Find the number of strings, modulo 998244353, that can result from applying the following operation on S between 0 and K times (inclusive):

* Choose a pair of integers i, j (1\leq i < j\leq |S|) such that the i-th and j-th characters of S are `0` and `1`, respectively. Remove the j-th character from S and insert it to the immediate left of the i-th character.

Constraints

* 1 \leq |S| \leq 300
* 0 \leq K \leq 10^9
* S consists of `0` and `1`.

Input

Input is given from Standard Input in the following format:


S K


Output

Find the number of strings, modulo 998244353, that can result from applying the operation on S between 0 and K times (inclusive).

Examples

Input

0101 1


Output

4


Input

01100110 2


Output

14


Input

1101010010101101110111100011011111011000111101110101010010101010101 20


Output

113434815

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
#define Reg register
#define RI Reg int
#define Con const
#define CI Con int&
#define I inline
#define W while
#define N 300
#define X 998244353
#define Inc(x,y) ((x+=(y))>=X&&(x-=X))
using namespace std;
int n,m,a[N+5],f[N+5][N+5][N+5];char s[N+5];
int main()
{
	RI i,j,k,cnt=1;for(scanf("%s",s+1),n=strlen(s+1),i=1;i<=n;++i) s[i]^'0'?++a[cnt]:++cnt;
	RI p;scanf("%d",&m),m=min(n,m),f[0][0][0]=1;
	for(i=0;i^cnt;++i) for(j=0;j<=m;++j) for(k=0;k<=m;++k) if(f[i][j][k])
	{
		Inc(f[i+1][j][k],f[i][j][k]);
		for(p=m-j;p;--p) Inc(f[i+1][j+p][k+p],f[i][j][k]);
		for(p=min(a[i+1],k);p;--p) Inc(f[i+1][j][k-p],f[i][j][k]);
	}
	RI t=0;for(i=0;i<=m;++i) Inc(t,f[cnt][i][0]);return printf("%d\n",t),0;
}