#include<set>
#include<map>
#include<list>
#include<iomanip>
#include<cmath>
#include<string>
#include<vector>
#include<queue>
#include<stack>
#include<complex>
#include<sstream>
#include<iostream>
#include<fstream>
#include<algorithm>
#include<numeric>
#include<utility>
#include<functional>
#include<stdio.h>
#include<assert.h>
#include<memory.h>
#include<bitset>
#include<math.h>

#define f first
#define s second
#define mp make_pair
#define pb push_back
#define lp(i,a,n) for(int i=(a);i<=(ll)(n);i++)
#define lpd(i,a,n) for(int i=(a);i>=(ll)(n);i--)
#define clr(a) memset(a,0,sizeof a)
#define all(v) v.begin(),v.end()
#define println(a) cout <<(a) <<endl
#define sz(x) ((int)(x).size())
#define mod 1000000007
#define eps 1e-6
#define infi 1e9
#define infll 1e16
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vll;
typedef set<int> si;
typedef map<int, int> mii;

const ll N = 100005 , UpperBound = 100000000000005ll;

ll n,k,arr[N];
int main(int argc, const char * argv[]) {

    scanf("%lld%lld" , &n,&k);

    lp(i, 1, n) scanf("%lld" , &arr[i]) , arr[i] += arr[i-1];


    if(1 == k) {
        printf("%lld\n" , n*(n+1ll)/2);
        return 0;
    }

    ll ans = 0 , b = k;
    k = 1;
    while (abs(k) < UpperBound) {
        if(!b) k = 0;
        map<ll,ll> prev;
        ++prev[0];
        lp(i, 1, n) {
            if(prev.count(arr[i]-k)) ans += prev[arr[i]-k];
            ++prev[arr[i]];
        }
        if(k == 0) break;
        k*=b;
    }

    printf("%lld\n",ans);
    return 0;
}