Bit Strings

#include <iostream>

using namespace std;

long long d[1010101];
const long long P = (1e9)+7;

long long modpow(long long b, long long e) {
		if (e == 0) return 1%P;
		long long u = modpow(b, e/2);
		u = (u*u)%P;
		if (e%2) u = (u*b)%P;
		return u;
}

int main() {
		d[0] = 1;
		long long n, k;
		cin >> n >> k;
		for (long long i = 1; i <= n; i++) {
				if (i < k) d[i] = modpow(2, i);
				else if (i == k) d[i] = (modpow(2, i)-(long long)1)%P;
				else d[i] = (d[i-1]*(long long)2 % P - d[i-k-1] % P + P) % P;
		}
		cout << d[n] << endl;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED