Bit Strings

#include <vector>
#include <iostream>
#include <algorithm>

using namespace std;
typedef long long LL;

vector<LL> cumsum { };
vector<LL> pows { };
vector<LL> nums { };

LL MOD = 1000000007;
int n,k;



LL norm(LL num) {
  while (num < 0) {
   num += MOD;
  }
  num = num % MOD;
  return num;
}

LL secondpow(LL pow) {
  if (pows.size() == 0) {
   pows.emplace_back(1);
   for (int i =0; i < 1000001; i++) {
     pows.emplace_back(norm(pows.back() * 2));
   }
  }
  return pows[pow];
}
int main() {
  cin >> n>>k;
  if (k == 1) {
    cout << 1 << endl;
    return 0;
  }  

  for (int i = 0; i < k; i++) {
    LL cur = secondpow(i);
    nums.emplace_back(cur);
  }
  
  cumsum = { 1 };
  for (int i = 1; i < k; i++) {
    LL ans = nums[i] + cumsum[i - 1];
    cumsum.emplace_back(norm(ans));
  }

//for (int i = 0; i < nums.size(); i++) cout << nums[i] << " "; cout<<endl;
//for (int i = 0; i < nums.size(); i++) cout << cumsum[i] << " "; cout<<endl;

  for (int i = k; i < n; i++) {
    LL previtem = (i == k) ? 0 : cumsum[i-k-1];
    LL newnum = cumsum.back() - previtem;
    nums.emplace_back(norm(newnum));
    LL newcumsum = norm(cumsum.back() + newnum);
    cumsum.emplace_back(newcumsum);
  }

//for (int i = 0; i < nums.size(); i++) cout << nums[i] << " "; cout<<endl;
//for (int i = 0; i < nums.size(); i++) cout << cumsum[i] << " "; cout<<endl;
  LL tmp = norm(secondpow(n) - nums.back());
  for (int i = nums.size() - k; i < n - 1; i++) {
    tmp = norm(tmp - nums[i]);
  }
  cout << norm(secondpow(n) - tmp);
  
}

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