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;

#define ll long long
#define all(aaa) aaa.begin(), aaa.end()

const int N = 305, MOD = 998244353;
int dp[N][N][N], a[N];

void add(int &a, int b) {
	a += b;
	if (a >= MOD)
		a -= MOD;
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);

	int n = 0, k;
	string s;
	cin >> s >> k;

	k = min(k, N - 1);

	for (const char &c : s) {
		if (c == '0')
			n++;
		else
			a[n]++;
	}

	n++;

	reverse(a, a + n);

	dp[0][0][0] = 1;

	for (int i = 0; i < n; i++) {
		for (int j = 0; j < N; j++) {
			for (int z = 0; z < N; z++) {
				if (dp[i][j][z]) {
					for (int h = 0; h <= a[i] + j; h++) {
						add(dp[i + 1][j + a[i] - h][z + max(0, a[i] - h)], dp[i][j][z]);
					}
				}
			}
		}
	}

	int ans = 0;

	for (int i = 0; i <= k; i++) {
		add(ans, dp[n][0][i]);
	}

	cout << ans << "\n";

	return 0;
}