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>
using namespace std;
const int mod=998244353;
int dp[305][305][305],n,k,ans=0,nxt[305];
char s[305];
int M(int x){return x>=mod?x-mod:x;}
int main()
{
	scanf("%s",s+1);
	n=strlen(s+1);
	scanf("%d",&k);
	dp[0][0][0]=1;
	nxt[n+1]=n+1;
	for(int i=n;i>0;i--)
	{
		if(s[i]=='0')nxt[i]=i;
		else nxt[i]=nxt[i+1];
	}
	for(int i=0;i<=n;i++)
	{
		for(int j=0;j<=i;j++)
		{
			if(j==n)continue;
			for(int k=0;k<=i;k++)
			{
				if(i<n)dp[i+1][j+1][k]=M(dp[i+1][j+1][k]+dp[i][j][k]);
				if(s[j+1]=='0'&&i<n)dp[i+1][j][k+1]=M(dp[i+1][j][k+1]+dp[i][j][k]);
				if(s[j+1]=='1'&&j<i)
				{
					if(i==n)dp[i][j+1][k]=M(dp[i][j+1][k]+dp[i][j][k]);
					else if(nxt[j+1]<=i+1)dp[i+1][nxt[j+1]][k]=M(dp[i+1][nxt[j+1]][k]+dp[i][j][k]);
				}
			}
		}
	}
	ans=0;
	for(int i=0;i<=min(n,k);i++)ans=M(ans+dp[n][n][i]);
	printf("%d\n",ans);
	return 0;
}