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 <stdio.h>
#include <bits/stdc++.h>

using namespace std;

const int MAXN = 305;
const int MOD = 998244353;

int n,K,N,ans;
int a[MAXN];
int f[MAXN][MAXN][MAXN];

char s[MAXN];

int main()
{
	scanf("%s%d",s + 1,&K);
	n = strlen(s + 1);
	int cnt = 0;
	for (int i = 1;i <= n;i++)
	{
		if (s[i] == '1')
			cnt++;
		else
		{
			a[++N] = cnt;
			cnt = 0;
		}
	}
	a[++N] = cnt;
	int sum = 0;
	for (int i = 2;i <= N;i++)
		sum += a[i];
	K = min(K,sum);
	f[0][0][0] = 1;
	for (int i = 0;i < N;i++)
		for (int j = 0;j <= K;j++)
			for (int k = 0;k <= j;k++)
				if (f[i][j][k])
				{
					(f[i + 1][j][k] += f[i][j][k]) %= MOD;
					for (int l = 1;l <= a[i + 1] && k + l <= j;l++)
						(f[i + 1][j][k + l] += f[i][j][k]) %= MOD;
					for (int l = 1;j + l <= K;l++)
						(f[i + 1][j + l][k] += f[i][j][k]) %= MOD;
				}
	for (int i = 0;i <= K;i++)
		(ans += f[N][i][i]) %= MOD;
	printf("%d\n",ans);
	return 0;
}