codeforces526D. Om Nom and Necklace【KMP】

# include "bits/stdc++.h"
using namespace std;
char str[(int)1e6 + 3];
int main() {
	ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	int n, k;
	while(~scanf("%d%d", &n, &k)) { 
	/*
	HINT: there exits a strange problem, which I guess results from the OJ
	The title is guaranteed to be a single group of data, but if it is normally processed as a single group, there will be no output on the platform, even if everything is normal locally. The following feedback will be given to us : 'wrong answer Unexpected EOF in the participants output'. 
	I was really surprised. After trying to change the language ( c++20 -> c++17 -> c++1 ), change bool to int... I had to query related questions online. I found that one blogger proposed the above solution, which was found to be effective in practice.
	If we encounter such problem in the future, perhaps we can solve them in the same way :)
	*/
		scanf("%s", str + 1); // well, it's a pity that (cin >> str + 1) will be judged wrong, even on CF
		int len = strlen(str + 1);
		int j = 0;
		vector<int> nxt(len + 1);
		for(int i = 2; i <= len; ++i) { // find nxt array in KMP to make use of its properties
			while(j && str[i] != str[j + 1]) j = nxt[j];
			if(str[i] == str[j + 1]) ++j;
			nxt[i] = j;
		}
		for(int i = 1; i <= len; ++i) {
			int cir = i - nxt[i]; // cir := minimum cyclic joint
			auto check = [&](int x, int cir) -> bool { 
				double L = (double) x / (double) ((double)(k + 1) * (double)cir); // infimum
				double R = (double) x / (double) ((double)k * (double)cir); // supremum
				return floor(R) >= ceil(L);
			};
			cout << check(i, cir);
		}
		cout << endl;
	}
	return 0;
}