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 meow(args...) fprintf(stderr, args)
typedef unsigned u32;
typedef unsigned long long u64;
const u32 P=998244353;
int cnt;
u32 f[301][301], g[301][301], h[301][301];
char s[305];
std::vector<int> a;
void ps() {
	for(int i=0; i<=cnt; ++i) {
		for(int j=0; j<=cnt; ++j) {
			g[i][j]=h[i][j]=f[i][j];
			if(i>0) g[i][j]=(g[i-1][j]+g[i][j])%P;
			if(i>0 && j>0) h[i][j]=(h[i-1][j-1]+h[i][j])%P;
		}
	}
}
int main() {
	int k;
	u32 ans=0;
	scanf("%s%d", s, &k);
	for(int i=0; s[i]; ++i) {
		if(s[i]=='0') {
			a.push_back(cnt);
			cnt=0;
		} else
			++cnt;
	}
	a.push_back(cnt);
	cnt=std::count(s, s+strlen(s), '1');
	f[0][0]=1;
	ps();
	for(int n: a) {
		for(int i=0; i<=cnt; ++i) {
			for(int j=0; j<=cnt; ++j)
				f[i][j]=(g[std::min(cnt, i+n)][j]+P-g[i][j]+h[i][j])%P;
		}
		ps();
	}
	for(int i=0; i<=cnt&&i<=k; ++i) ans=(ans+f[0][i])%P;
	printf("%u\n", ans);
	return 0;
}