cf776c

//sum[r]=sum[l]+kk;
//ans+=mp[sum[i]-kk];其实是个dp 
#include<bits/stdc++.h>
using namespace std;
#define ll long long 
#define maxn 100005

int n,a[maxn];
ll ans,kk,k,sum[maxn];

void solve(ll kk){
    map<ll,int>mp;
    for(int i=0;i<=n;i++){
        mp[sum[i]]++;
        ans+=mp[sum[i]-kk];
    }
}

int main(){
    scanf("%d%lld",&n,&k);
    sum[0]=ans=0;
    for(int i=1;i<=n;i++){
        scanf("%d",&a[i]);
        sum[i]=sum[i-1]+a[i];
    } 
    if(k==1){
        solve(1);
        printf("%lld\n",ans);
        return 0;
    }
    if(k==-1){
        solve(1);solve(-1);
        printf("%lld\n",ans);
        return 0;
    }
    
    kk=1;
    while(kk<=(ll)1000000000*n){
        solve(kk);
        kk*=k;        
    }
    printf("%lld\n",ans);
    return 0;
}