#include <bits/stdc++.h>
using namespace std;
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
long long a[100005] = {};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, k;
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    a[i] += a[i - 1];
  }
  long long ans = 0;
  unordered_map<long long, int, custom_hash> mp;
  mp[0] = 1;
  for (int i = 1; i <= n; i++) {
    if (k == 1) {
      if (mp.find(a[i] - 1) != mp.end()) {
        ans += mp[a[i] - 1];
      }
    } else if (k == -1) {
      if (mp.find(a[i] + 1) != mp.end()) {
        ans += mp[a[i] + 1];
      }
      if (mp.find(a[i] - 1) != mp.end()) {
        ans += mp[a[i] - 1];
      }
    } else {
      long long p = 1;
      while (p <= 1e15) {
        if (mp.find(a[i] - p) != mp.end()) {
          ans += mp[a[i] - p];
        }
        p *= k;
      }
    }
    mp[a[i]]++;
  }
  cout << ans << endl;
  return 0;
}
