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 rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;
typedef pair<int,int>P;

const int MOD=998244353;
const int INF=0x3f3f3f3f;
const ll INFL=0x3f3f3f3f3f3f3f3f;

ll dp[400][400][400];
int a[400];
int d[400];

int main(){
	string s;cin>>s;
	int K;cin>>K;
	int n=0;
	int cnt=0;
	for(char c:s){
		if(c=='0')cnt++;
		else a[n++]=cnt;
	}
	rep(i,n){
		d[a[i]]++;
	}
	K=min(K,n);
	dp[cnt+1][0][0]=1;
	for(int i=cnt+1;i>=1;i--)rep(j,K+1)rep(k,n+1){
		if(dp[i][j][k]==0)continue;
		for(int t=0;t<=d[i-1]+k;t++){
			int nj=j+max(0,d[i-1]-t);
			//~ if(nj>K)break;
			(dp[i-1][nj][d[i-1]+k-t]+=dp[i][j][k])%=MOD;
		}
	}
	ll ans=0;
	rep(i,K+1){
		(ans+=dp[0][i][0])%=MOD;
	}
	cout<<ans<<endl;
}