#pragma GCC optimize("Ofast")

#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <random>

using namespace std;
using namespace __gnu_pbds;

typedef
tree<pair<int, int>, null_type, less<pair<int, int>>, rb_tree_tag, tree_order_statistics_node_update> orderedSet;

#define pb push_back
#define F first
#define S second
#define all(a) (a).begin(), (a).end()

#define for1(i0, l0, r0) for (int i0 = l0; i0 < r0; ++i0)
#define for2(i0, l0, r0) for (int i0 = l0; i0 <= r0; ++i0)
#define forn(i0, n0) for (int i0 = 0; i0 < n0; ++i0)
#define forn1(i0, n0) for (int i0 = 1; i0 < n0; ++i0)
#define forr(i0, n0) for (int i0 = n0; i0 >= 0; --i0)
#define forr1(i0, r0, l0) for (int i0 = r0; i0 > l0; --i0)
#define forr2(i0, r0, l0) for (int i0 = r0; i0 >= l0; --i0)

#define Sort(a) sort(all(a))
#define Reverse(a) reverse(all(a))
#define relaxMax(a, b) a = max(a, b)
#define relaxMin(a, b) a = min(a, b)

typedef long long ll;
typedef long double ld;
#define ui unsigned int
#define ull unsigned long long

typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
typedef pair<string, string> pss;

typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<double> vd;
typedef vector<ld> vld;
typedef vector<bool> vb;
typedef vector<string> vs;

typedef vector<pii> vpii;
typedef vector<pll> vpll;
typedef vector<pdd> vpdd;

typedef vector<vi> vvi;
typedef vector<vd> vvd;
typedef vector<vll> vvll;
typedef vector<vb> vvb;

#define vpss vector<pss>
#define vvs vector<vs>
#define vvpii vector<vpii>
#define vvpll vector<vpll>
#define vpt vector<pt>
#define vvvi vector<vvi>
#define vsi vector<set<int>>
#define ss second
#define ff first

#define printvi(arr) for (int x0 : arr) cout << x0 << ' '; cout << '\n';
#define printvll(arr) for (ll x0 : arr) cout << x0 << ' '; cout << '\n';
#define printpair(pair0) cout << pair0.F << ' ' << pair0.S << '\n';
#define printvp(arr) for (auto pair0 : arr) printpair(pair0);
#define initArray(arr, N0, X0) memset(arr, X0, N0 * sizeof(int))
//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

void init() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    //cout.precision(16);
    //freopen("amusing.in", "r", stdin);
    //freopen("amusing.out", "w", stdout);
}

const ll mod = 998244353;

void solve() {
    string s;
    int k;
    cin >> s >> k;
    s += "0";
    int n = s.length();
    vi a;
    forn(i, n){
        if (s[i] == '0'){
            int cnt = 0;
            while (i - cnt > 0 && s[i - cnt - 1] == '1') cnt++;
            a.pb(cnt);
        }
    }
    int m = a.size();
    int sum = 0;
    for (int x : a) sum += x;
    vi suf(m + 1);
    for (int i = m - 1; i >= 0; --i) suf[i] = a[i] + suf[i + 1];
    int N = 2 * min(k, sum) + 1;
    vector<vvll> dp(m + 1, vvll(sum + 1, vll(N)));
    dp[m][0][0] = 1;
    for (int i = m - 1; i >= 0; --i){
        forn(x, n){
            forn(sum0, 1 + suf[i + 1]){
                if (x + sum0 > suf[i]) break;
                forn(abs0, min(N, 2 * suf[i + 1] + 1)){
                    int abs1 = abs0 + abs(x - a[i]);
                    if (abs1 >= N) break;
                    dp[i][x + sum0][abs1] += dp[i + 1][sum0][abs0];
                    dp[i][x + sum0][abs1] %= mod;
                }
            }
        }
    }
    ll ans = 0;
    forn(a, N){
        ans += dp[0][sum][a];
        ans %= mod;
    }
    cout << ans << '\n';
}

bool multitest = false;

int main() {
    init();
    int t = 1;
    if (multitest) cin >> t;
    forn(i, t) solve();
}

Measured memory_bytes: 57596