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>

const int N = 305, djq = 998244353;

char s[N];
int K, len, n, c[N], f[N][N][N], sum[N], s1[N][N], s2[N][N], ans;

int main()
{
	scanf("%s", s + 1); std::cin >> K;
	len = strlen(s + 1); n = 1;
	for (int i = 1; i <= len; i++) (s[i] == '1' ? c[n] : n)++;
	for (int i = 1; i <= n; i++) sum[i] = sum[i - 1] + c[i];
	f[0][0][0] = 1;
	for (int i = 1; i <= n; i++)
	{
		for (int j = 0; j <= sum[n]; j++)
			for (int k = 0; k <= sum[n]; k++)
			{
				s1[j][k] = s2[j][k] = f[i - 1][j][k];
				if (j) s1[j][k] = (s1[j][k] + s1[j - 1][k]) % djq;
				if (j && k) s2[j][k] = (s2[j][k] + s2[j - 1][k - 1]) % djq;
			}
		for (int j = sum[i]; j <= sum[n]; j++)
			for (int k = 0; k <= j; k++)
			{
				f[i][j][k] = s1[j][k];
				if (j > c[i])
				{
					f[i][j][k] = (f[i][j][k] - s1[j - c[i] - 1][k] + djq) % djq;
					if (k) f[i][j][k] = (f[i][j][k] + s2[j - c[i] - 1][k - 1]) % djq;
				}
			}
	}
	for (int i = 0; i <= K && i <= sum[n]; i++) ans = (ans + f[n][sum[n]][i]) % djq;
	return std::cout << ans << std::endl, 0;
}