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;

int d[333][666][666];
vector<int> u;
int p = 998244353;
int f(int i, int v, int w) {
    if(!i)
        return v ? 0 : 1;
    if(v > w)
        return 0;
    if(d[i][v][w] >= 0)
        return d[i][v][w];
    d[i][v][w] = 0;
    for(int j = max(-u[i - 1], -w); j <= v; j++)
        (d[i][v][w] += f(i - 1, v - j, w - abs(j))) %= p;
    return d[i][v][w];
}
int main() {
    string s;
    int k;
    cin >> s >> k;
    k = min(k, 300);
    k += k;
    for(s += '0';;) {
        auto i = s.find('0');
        if(i == -1)
            break;
        s = s.substr(i + 1);
        u.push_back(i);
    }
    for(int i = 0; i < 333; i++)
        for(int j = 0; j <= k; j++)
            for(int w = 0; w <= k; w++)
                d[i][j][w] = -1;
    cout << f(u.size(), 0, k) << endl;
    return 0;
}