Bit Strings

#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;

constexpr ll mod = 1e9+7;

ll sums[10001000];

ll get(int i) {
    if (i < 0) return 0;
    return sums[i];
}

ll mpow(ll b, ll e) {
    if (e == 0) return 1;
    if (e == 1) return b;
    if (e % 2 == 0) {
        ll p = mpow(b, e/2);
        return (p * p) % mod;
    }
    return (b * mpow(b, e-1)) % mod;
}

int main() {
    cin.sync_with_stdio(false);
    cin.tie(nullptr);
    
    ll n, k;
    cin >> n >> k;
    if (n == k) {
        cout << (mpow(2, n) + mod - 1) % mod << endl;
        return 0;
    }
    for (ll i = 1; i < k; i++) {
        sums[i] = (get(i-1) + mpow(2, i)) % mod;
    }
    sums[k] = (get(k-1) + mpow(2, k) + mod - 1) % mod;
    //for (int i = 0; i <= n; i++) cerr << sums[i] << " ";
    //cout<<endl;
    for (ll i = k+1; i <= n; i++) {
        sums[i] = (get(i-1) + get(i-1) - get(i-k-1) + mod) % mod;
    }
    //for (int i = 0; i <= n; i++) cerr << sums[i] << " ";
    cout << (get(n) - get(n-1) + mod) % mod << endl;
    /*
    ll n, k;
    cin >> n >> k;
    ll res = 0;
    for (ll i = 0; i < (1<<n); i++) {
        for (int j = 0; j <= n-k; j++) {
            if (!((i >> j) & ((1 << k) - 1))) goto skip;
        }
        res++;
        skip:;
    }
    cout << res << 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