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>
using namespace std;
const int N=305,mo=998244353;
int n,K,i,j,k,l,f[N][N][N],a[N],ps[N],m,ans;
char c[N];
int main(){
	scanf("%s%d",c+1,&K);n=strlen(c+1);
	m=1;for(i=1;i<=n;++i)if(c[i]=='0')++m;else ++a[m];
	f[0][0][0]=1;
	for(i=1;i<=m;++i){
		for(j=0;j<=n;++j)for(k=0;k<=n;++k)
			f[i][j][k]=(f[i-1][j][k]+(j && k?f[i][j-1][k-1]:0))%mo;
		for(j=0;j<=n;++j){
			for(k=n;k>=0;--k)ps[k]=(f[i-1][j][k]+ps[k+1])%mo;
			for(k=0;k<=n;++k)f[i][j][k]=(f[i][j][k]+1ll*mo+ps[k+1]-ps[min(n+1,k+a[i]+1)])%mo;
		}
	}
	for(j=0;j<=min(K,n);++j)ans=(ans+f[m][j][0])%mo;
	printf("%d\n",ans);
}