#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#include <string>
#include <math.h>
#include <iomanip>
#include <limits>
#include <list>
#include <queue>
#include <tuple>
#include <map>
#include <stack>
#include <set>
#include <bitset>
#include <functional>
#include <cassert>
using namespace std;
#define fast_io ios_base::sync_with_stdio (false) ; cin.tie(0) ; cout.tie(0) ;
#define ll long long int
#define rep(i,n) for(int i=0; i<(int)(n); i++)
#define reps(i,n) for(int i=1; i<=(int)(n); i++)
#define REP(i,n) for(int i=n-1; i>=0; i--)
#define REPS(i,n) for(int i=n; i>0; i--)
#define MOD (long long int)(998244353)
#define INF (int)(1e9)
#define LINF (long long int)(1e18)
#define chmax(a, b) a = (((a)<(b)) ? (b) : (a))
#define chmin(a, b) a = (((a)>(b)) ? (b) : (a))
#define all(v) v.begin(), v.end()
typedef pair<int, int> Pii;
typedef pair<ll, ll> Pll;

ll mpow(ll a, ll b){
  if(b==0) return 1;
  else if(b%2==0){ll memo = mpow(a,b/2); return memo*memo%MOD;}
  else return mpow(a,b-1) * a % MOD;
}
ll lpow(ll a, ll b){
  if(b==0) return 1;
  else if(b%2==0){ll memo = lpow(a,b/2); return memo*memo;}
  else return lpow(a,b-1) * a;
}
ll gcd(ll a, ll b){
  if(b==0) return a;
  else return gcd(b, a%b);
}
vector<ll> kaijo_memo;
ll kaijo(ll n){
  if(kaijo_memo.size() > n) return kaijo_memo[n];
  if(kaijo_memo.size() == 0) kaijo_memo.push_back(1);
  while(kaijo_memo.size() <= n) kaijo_memo.push_back(kaijo_memo[kaijo_memo.size()-1] * kaijo_memo.size() % MOD);
  return kaijo_memo[n];
}
vector<ll> gyaku_kaijo_memo;
ll gyaku_kaijo(ll n){
  if(gyaku_kaijo_memo.size() > n) return gyaku_kaijo_memo[n];
  if(gyaku_kaijo_memo.size() == 0) gyaku_kaijo_memo.push_back(1);
  while(gyaku_kaijo_memo.size() <= n) gyaku_kaijo_memo.push_back(gyaku_kaijo_memo[gyaku_kaijo_memo.size()-1] * mpow(gyaku_kaijo_memo.size(), MOD-2) % MOD);
  return gyaku_kaijo_memo[n];
}

ll nCr(ll n, ll r){
  if(n == r) return 1;//0個の丸と-1個の棒みたいな時に時に効く？不安.
  if(n < r || r < 0) return 0;
  ll ret = 1;
  if(n <= 1e7){
    ret *= kaijo(n); ret %= MOD;
    ret *= gyaku_kaijo(r); ret %= MOD;
    ret *= gyaku_kaijo(n-r); ret %= MOD;
  }else{
    rep(i,r){
      ret *= n-i; ret %= MOD;
      ret *= mpow(r-i, MOD-2); ret %= MOD;
    }
  }
  return ret;
}

ll dp[310][310][310] = {};
ll imos[310][310][310] = {};
ll gyaku[310][310][310] = {};

int main(void){
  fast_io
  cout<<fixed<<setprecision(15);

  string S; ll K;
  cin>>S>>K;
  chmin(K,300);
  while(S.size() > 0 && S.back() == '0'){
    S.pop_back();
  }
  if(S.size() == 0){
    cout<<1<<endl;
    return 0;
  }

  vector<ll> A;
  REP(i,S.size()){
    int count = 0;
    /*
    if(S[i] == '0'){
      A.push_back(0);
      continue;
    }
    */
    while(S.size() > 0 && S[i] == '1'){
      i--;
      count++;
      S.pop_back();
    }
    //i++;
    A.push_back(count);
  }
  if(S[0] == '0') A.push_back(0);
/*
  rep(i,A.size()){
    cout<<A[i]<<" ";
  }
  cout<<endl;
  */

  dp[0][0][0] = 1;
  int n = A.size();
  rep(i,n){
    rep(j,K+1){
      rep(k,K+1){
        if(A[i] > 0 && K-j > 0){
          imos[i+1][j+1][k+1] += dp[i][j][k];
          imos[i+1][j+1][k+1] %= MOD;
          ll x = min(K-j, A[i]);
          imos[i+1][j+x+1][k+x+1] += MOD - dp[i][j][k];
          imos[i+1][j+x+1][k+x+1] %= MOD;
        }

        gyaku[i+1][j][k] += dp[i][j][k];
        gyaku[i+1][j][k] %= MOD;
      }
    }

    rep(j,K+1){
      rep(k,K+1){
        if(j-1 >= 0 && k-1 >= 0){
          imos[i+1][j][k] += imos[i+1][j-1][k-1];
          imos[i+1][j][k] %= MOD;
          dp[i+1][j][k] += imos[i+1][j][k];
          dp[i+1][j][k] %= MOD;
        }
      }
    }

    rep(j,K+1){
      REP(k,K+1){
        gyaku[i+1][j][k] += gyaku[i+1][j][k+1];
        gyaku[i+1][j][k] %= MOD;
        dp[i+1][j][k] += gyaku[i+1][j][k];
        dp[i+1][j][k] %= MOD;
      }
    }
  }

  ll ans = 0;
  rep(j,K+1){
    ans += dp[n][j][0];
    ans %= MOD;
  }

  cout << ans << endl;
/*
  rep(i,n+1){
    rep(j,2){
      rep(k,2){
        cout<<dp[i][j][k]<<" ";
      }
    }
    cout<<endl;
  }
*/
  return 0;
}

Measured memory_bytes: 335316