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 maxN = 305, mod = 998244353;

int n, m;
int f[2][maxN + 1][maxN + 1];
int a[maxN + 1], cnt;
char s[maxN + 1];

inline void update(int &x, int y) { x = x + y >= mod ? x + y - mod : x + y; }

int main()
{
	scanf("%s %d", s + 1, &m);
	n = strlen(s + 1); m = min(m, n);

	int l = 1;
	while(l <= n)
	{
		int r = l;
		while(r <= n && s[r] == '1') r ++;
		a[++ cnt] = r - l;
		l = r + 1;
	}

	int now = 0;
	f[now][0][0] = 1;
	for(int i = cnt; i >= 1; i--)
	{
		now ^= 1;
		memset(f[now], 0, sizeof(f[now]));
		for(int j = 0; j <= m; j++)
			for(int k = 0; k <= j; k++)
			{
				if(!f[now ^ 1][j][k]) continue;
				int res = f[now ^ 1][j][k];
				for(int t = 0; t <= a[i]; t++) update(f[now][j + t][k + t], res);
				for(int t = 1; t <= k; t++) update(f[now][j][k - t], res);
			}
	}

	int ans = 0;
	for(int i = 0; i <= m; i++) update(ans, f[now][i][0]);
	
	printf("%d\n", ans);
	return 0;
}