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;

typedef long long ll;

string S;
ll N;
ll K;
vector<ll> A;
ll M;
vector<vector<vector<ll>>> Dp;
const ll MOD = 998244353;
ll Res;

int main() {
  cin >> S >> K;
  N = S.size();
  K = min(N, K);
  reverse(S.begin(), S.end());
  ll now = 0;
  for (char c : S) {
    if (c == '0') {
      A.push_back(now);
      now = 0;
    } else {
      ++now;
    }
  }
  A.push_back(now);
  M = A.size();
  Dp.resize(M + 1);
  for (auto &Dpi : Dp) {
    Dpi.resize(N + 1);
    for (auto &Dpij : Dpi) Dpij.resize(K + 1);
  }
  Dp[0][0][0] = 1;
  for (ll i = 0; i < M; ++i) {
    for (ll j = N; j >= 0; --j) {
      for (ll k = 0; k <= K; ++k) {
        (Dp[i + 1][j][k] += Dp[i][j][k]) %= MOD;
        if (j != N) {
          (Dp[i + 1][j][k] += Dp[i + 1][j + 1][k]) %= MOD;
        }
      }
    }
    for (ll j = 0; j <= N; ++j) {
      for (ll k = 0; k <= K; ++k) {
        for (ll a = 1; a <= A[i] && j + a <= N && k + a <= K; ++a) {
          (Dp[i + 1][j + a][k + a] += Dp[i][j][k]) %= MOD;
        }
      }
    }
  }
  for (ll k = 0; k <= K; ++k) {
    (Res += Dp[M][0][k]) %= MOD;
  }
  cout << Res << endl;
  return 0;
}