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<cstdio>
#include<cstring>
#include<algorithm>
#define P 998244353
#define N 305

char s[N];
int n,m;

int cnt[N];

int dp[N][N][N<<1],s1[N][N<<1],s2[N][N<<1],ans;

int main(){
	scanf("%s%d",s+1,&m);
	n=strlen(s+1);
	m=std::min(m,n)<<1;
	for(int i=1,tmp=0;i<=n;i++)
		if(s[i]=='0')
			tmp++;
		else
			cnt[tmp+1]++;
	dp[0][0][0]=1;
	for(int j=0;j<=n&&j<=m;j++)
		s1[j+1][j+1]=1;
	s2[1][1]=1; 
	for(int i=1;i<=n+1;i++){
		for(int j=0;j<=n;j++)
			for(int k=0;k<=m;k++){
				dp[i][j][k]=(dp[i][j][k]+s1[j+1][k+1])%P;
				int x=std::min(std::min(n-j,k),cnt[i]);
				if(x)
					dp[i][j][k]=((dp[i][j][k]+s2[j+2][k])%P+P-s2[j+2+x][k-x])%P;
			}
		for(int j=0;j<=n;j++)
			for(int k=0;k<=m;k++)
				s1[j+1][k+1]=(s1[j][k]+dp[i][j][k])%P;
		for(int j=n;j>=0;j--)
			for(int k=0;k<=m;k++)
				s2[j+1][k+1]=(s2[j+2][k]+dp[i][j][k])%P;
	}
	for(int k=0;k<=m;k++)
		ans=(ans+dp[n+1][0][k])%P;
	printf("%d",ans);
}