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:
// M
#include<bits/stdc++.h>
using namespace std;
const int N = 303, Mod = 998244353;
int n, k, C[N], dp[N][N][N];
inline void Add(int &a, int b)
{
	a += b;
	if (a >= Mod)
		a -= Mod;
}
int main()
{
	string S;
	cin >> S >> k;
	S = "0" + S;
	for (int i = 0; i < (int)S.size();)
	{
		int r = i + 1;
		while (r < (int)S.size() && S[r] == '1')
			r ++;
		C[n ++] = r - i - 1;
		i = r;
	}
	k = min(k, (int)S.size());
	dp[n][0][0] = 1;
	int sm = 0;
	for (int i = n - 1; ~ i; sm += C[i], i --)
		for (int j = sm; j >= 0; j --)
		{
			for (int h = 0; h <= k; h ++)
				Add(dp[i][j][h], dp[i][j + 1][h]),
				Add(dp[i][j][h], dp[i + 1][j][h]);
			for (int h = 0; h <= k; h ++)
				for (int df = 1; df <= C[i]; df ++)
					Add(dp[i][j + df][h + df], dp[i + 1][j][h]);
		}
	int tot = 0;
	for (int h = 0; h <= k; h ++)
		Add(tot, dp[0][0][h]);
	return !printf("%d\n", tot);
}