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;
const int MAXN = 305;

char s[MAXN];
int n, k, nxt[MAXN], dp[MAXN][MAXN][MAXN];

int main(){	
	scanf("%s %d", s, &k);
	n = strlen(s);
	k = min(n, k);
	
	for(int i = n; i >= 0; i--){
		if(i == n)nxt[i] = i;
		else if(s[i] == '0')nxt[i] = i;
		else nxt[i] = nxt[i + 1];
	}
	
	for(int i = n; i >= 0; i--)
	for(int j = n; j >= 0; j--)
	for(int r = 0; r <= k; r++){
		if(i == n){
			if(j == 0)dp[i][j][r] = 1;
			else dp[i][j][r] = 0;
		}else{
			if(s[i] == '0'){
				dp[i][j][r] = dp[i + 1][j][r];
				if(r > 0 && j + 1 <= n)dp[i][j][r] = (dp[i][j][r] + dp[i][j + 1][r - 1]) % MOD;
			}else{
				dp[i][j][r] = dp[i + 1][j][r];
				if(j >= nxt[i] - i)dp[i][j][r] = (dp[i][j][r] + dp[(nxt[i] == n ? n : nxt[i] + 1)][j - (nxt[i] - i)][r]) % MOD;
			}
		}
	}
	
	printf("%d\n", dp[0][0][k]);
	
	return 0;
}