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 = 303;
const int mod = 998244353;

string S;
int k;
int dp[Maxn][Maxn][Maxn];
int res;

int main()
{
    cin >> S >> k;
    int lst = -1;
    int cur = 0;
    dp[cur][0][0] = 1;
    for (int i = 0; i < S.length(); i++) if (S[i] == '0') {
        int ones = i - 1 - lst;
        for (int j = 0; j < Maxn; j++)
            for (int l = 0; l < Maxn; l++) if (dp[cur][j][l])
                for (int t = 0; t <= S.length(); t++) {
                    int lv = max(0, ones - t);
                    if (lv > j) continue;
                    int add = max(0, t - ones);
                    if (j - lv + add >= Maxn || l + add >= Maxn) continue;
                    dp[cur + 1][j - lv + add][l + add] = (dp[cur + 1][j - lv + add][l + add] + dp[cur][j][l]) % mod;
                }
        lst = i; cur++;
    }
    int ones = int(S.length()) - 1 - lst;
    for (int j = 0; j <= ones; j++)
        for (int l = 0; l < Maxn && l <= k; l++)
            res = (res + dp[cur][j][l]) % mod;
    printf("%d\n", res);
    return 0;
}