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 mod=998244353;
inline void Add(int &a,int b){a=a+b>=mod?a+b-mod:a+b;}
char s[301];int n,k;
int f[301][301][301];
int cnt[301],tot,now=0,suf[302];
int main()
{
	scanf("%s%d",s+1,&k);n=strlen(s+1);k=min(k,n);
	for(int i=1;i<=n;i++)
	{
		if(s[i]=='0') cnt[++tot]=now,now=0;
		else now++;
	}
	if(now) cnt[++tot]=now;
	for(int i=tot;i;i--) suf[i]=suf[i+1]+cnt[i];
	f[0][0][0]=1;
	for(int i=1;i<=tot;i++)
	{
		for(int lst=0;lst<=n;lst++) for(int st=0;st<=k;st++) if(f[i-1][lst][st])
		{
			for(int v=0;v<=cnt[i];v++) if(lst>=cnt[i]-v&&lst-cnt[i]+v<=suf[i+1])
				Add(f[i][lst-cnt[i]+v][st],f[i-1][lst][st]);
			for(int v=cnt[i]+1;lst+v-cnt[i]<=suf[i+1];v++)
				Add(f[i][lst+v-cnt[i]][st+v-cnt[i]],f[i-1][lst][st]);
		}
	}
	int ans=0;
	for(int i=0;i<=k;i++) Add(ans,f[tot][0][i]);
	cout<<ans<<endl;
}