#include <string>
#include <vector>
#include <algorithm>
#include <numeric>
#include <set>
#include <map>
#include <queue>
#include <iostream>
#include <sstream>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstring>
#include <cctype>
#include <cassert>
#include <limits>
#include <functional>
#define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i))
#define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i))
#define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i))
#if defined(_MSC_VER) || __cplusplus > 199711L
#define aut(r,v) auto r = (v)
#else
#define aut(r,v) __typeof(v) r = (v)
#endif
#define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it)
#define all(o) (o).begin(), (o).end()
#define pb(x) push_back(x)
#define mp(x,y) make_pair((x),(y))
#define mset(m,v) memset(m,v,sizeof(m))
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
using namespace std;
typedef vector<int> vi; typedef pair<int,int> pii; typedef vector<pair<int,int> > vpii; typedef long long ll;
template<typename T, typename U> inline void amin(T &x, U y) { if(y < x) x = y; }
template<typename T, typename U> inline void amax(T &x, U y) { if(x < y) x = y; }

int main() {
	int N; int K;
	while(~scanf("%d%d", &N, &K)) {
		string S;
		cin >> S;
		ll l = 0, u = K;
		while(u - l > 0) {
			ll mid = (l + u) / 2;
			ll k = K;
			int pos = 0;
			vector<pair<ll, ll> > memo(N, mp(-1, -1LL));
			bool last = false;
			for(ll i = 0; i < mid && k > 0; ++ i) {
				if(!last && memo[pos].first != -1) {
					ll j = memo[pos].first;
					ll len = i - j;
					ll cnt = memo[pos].second - k;
					ll cycles = (mid - i) / len;
					k -= min(k, cycles * cnt);
					i += cycles * len;
					last = true;
					-- i;
					continue;
				}
				memo[pos] = mp(i, k);
				int num = 1;
				int start = pos;
				while(num > 0 && k > 0) {
					-- k;
					num += S[pos] - '0' - 1;
					if(++ pos == N) pos = 0;
					if(num > 0 && pos == start) {
						k = 0;
						break;
					}
				}
			}
			if(k == 0)
				u = mid;
			else
				l = mid + 1;
		}
		printf("%lld\n", u);
	}
	return 0;
}