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 <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int mod = 998244353;
int f[305][305][305], n, m, a[305];
char s[305];
inline int abs(const int &x){return x<0?-x:x;}
inline int add(const int &x, const int &y){return x+y>=mod?x+y-mod:x+y;}
int main() {
	scanf("%s%d",s+1,&m);
	for(int i=1, L=strlen(s+1), pre=0;i<=L;i++) {
		if(s[i]=='0') {
			a[++n]=i-pre-1;
			pre=i;
		} else if(i==L) {
			a[++n]=i-pre;
		}
	}
	m=min(m,int(strlen(s+1)));
	f[n+1][0][0]=1;
	for(int i=n+1;i>1;i--) {
		for(int p=0;p<=m;p++) {
			for(int j=0;j<=m;j++) if(f[i][p][j]){
				for(int k=0;k<=m;k++) {
					if(k<=p) {
						f[i-1][p-k][j]=add(f[i][p][j],f[i-1][p-k][j]);
					}
					if(k<=a[i-1]&&k) {
						f[i-1][p+k][j+k]=add(f[i][p][j],f[i-1][p+k][j+k]);
					}
				}
			}
		}
	}
	int ans=0;
	for(int i=0;i<=m;i++) ans=add(ans,f[1][0][i]);
	printf("%d\n",ans);
	return 0;
}