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;
inline void Add(int &x, int y) { x += y; if (x >= mod) x -= mod; }
char s[305];
int len, n, K, a[305], f[305][305][305];
int main() {
	scanf("%s %d", s + 1, &K);
	len = strlen(s + 1);
	n = 0;
	for (int i = 1, lst = 0; i <= len + 1; i++) {
		if (i == len + 1 || s[i] == '0') {
			a[++n] = i - lst - 1;
			lst = i;
		}
	}
	reverse(a + 1, a + 1 + n);
	f[0][0][0] = 1;
	int ps = 0;
	for (int i = 1; i <= n; i++) {
		for (int j = 0; j <= ps; j++) {
			for (int k = 0; k <= ps; k++) if (f[i - 1][j][k]) {
				for (int l = 0; l <= a[i]; l++) {
					Add(f[i][j + a[i] - l][k + a[i] - l], f[i - 1][j][k]);
				}
			}
		}
		for (int k = 0; k <= ps; k++) {
			int sum = 0;
			for (int j = ps; j >= 0; j--) {
				Add(f[i][j][k], sum);
				Add(sum, f[i - 1][j][k]);
			}
		}
		ps += a[i];
	}
	int ans = 0;
	for (int k = 0; k <= min(K, ps); k++) {
		Add(ans, f[n][0][k]);
	}
	printf("%d\n", ans);
	return 0;
}