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>
char s[305];
int n=0,len,k,a[305],b[305],mod=998244353;
long long f[305][305][305];
int main(){
	
	std::cin>>s>>k;
	len=strlen(s);
	n=1;
	for (int i=0;i<len;++i) {
		if (s[i]=='0') ++n;
		else ++a[n];
	}
	++n; 
	for (int i=n-1;i>=0;--i) b[i]=b[i+1]+a[i];
	k=std::min(b[1],k);
	f[0][0][0]=1;
	for (int i=1;i<=n;++i) {
		for (int c=0;c<=a[i];++c){
			for (int j=c;j<=k;++j) {
				for (int l=j;l<=k;++l) {
					f[i][l][j-c]=(f[i][l][j-c]+f[i-1][l][j])%mod;
				}
			}
		}
		for (int c=1;c<=k;++c){
			for (int j=k-c;j>=0;--j) {
				for (int l=0;l<=j;++l) {
					f[i][j+c][l+c]=(f[i][j+c][l+c]+f[i-1][j][l])%mod;
				}
			}
		}
	}
	long long ans=0;
	for (int i=0;i<=k;++i) ans+=f[n][i][0];
	printf("%lld",ans%mod);
	
	return 0;
}