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 <iostream>
#include <algorithm>
#include <vector>
#include <string.h>

constexpr int str_length = 300;
char S[str_length + 10];

constexpr int mod = 998244353;
int DP[str_length + 1][str_length + 1];
int EP[str_length + 1][str_length + 1];

int main(void){
    int K; std::cin >> S >> K;
    const int n = strlen(S);
    std::vector<int> A(0); A.reserve(n);
    int sum = 0;
    for(int i = 0; i < n; ){
        int cnt = 0; while(i + cnt < n and S[i + cnt] == '1') ++cnt;
        A.push_back(cnt); i += cnt + 1; sum += cnt;
    }

    std::reverse(A.begin(), A.end());
    const int m = A.size();
    DP[0][0] = 1;
    for(int i = 0; i < m; ++i){
        std::memset(EP, 0, sizeof(EP));
        for(int chokin = 0; chokin <= sum; ++chokin){
            for(int k = 0; k <= sum; ++k) if(DP[chokin][k]){
                for(int move = (-k < -chokin) ? -chokin : -k; move <= A[i]; ++move){
                    const int nxt_k = ((0 < move) ? move : 0) + k;
                    if(nxt_k > K) continue;
                    (EP[chokin + move][nxt_k] += DP[chokin][k]) %= mod;
                }
            }
        }
        std::swap(DP, EP);
    }
    int res = 0;
    for(int i = 0; i <= sum; ++i){ res += DP[0][i]; if(res >= mod) res -= mod; }
    std::cout << res << '\n';
    return 0;
}