#include <bits/stdc++.h>
using namespace std;
const long long int mod = 1e9 + 7;
const long long int lim = 1e17;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int T = clock();
  long long int n, k;
  cin >> n >> k;
  map<long long int, long long int> mpp;
  vector<long long int> a(n);
  for (long long int i = 0; i < n; i++) cin >> a[i];
  long long int tot = 0;
  mpp[0] = 1;
  long long int ans = 0;
  for (long long int i = 0; i < n; i++) {
    tot += a[i];
    long long int r = 1;
    if (k == -1) {
      ans += mpp[tot - 1];
      ans += mpp[tot + 1];
    } else if (k == 1)
      ans += mpp[tot - 1];
    else {
      while (r < lim) {
        if (mpp.find(tot - r) != mpp.end()) ans += mpp[tot - r];
        r *= k;
      }
    }
    mpp[tot]++;
  }
  cout << ans;
  cerr << "\n\nTIME: " << (double)(clock() - T) / CLOCKS_PER_SEC << " sec\n";
  T = clock();
  return 0;
}
