#include "biscuits.h"
#include "bits/stdc++.h"
using namespace std;
bool check(long long x, __int128 y, std::vector<long long> a) {
int k = a.size();
for(long long i=0; i<x; i++) {
__int128 w = y;
for(int j=k-1; j>=0; j--) {
__int128 nd = w / (1ll << j);
nd = min(nd, (__int128) a[j]);
a[j] -= nd;
w -= nd * (1ll << j);
}
if(w) return 0;
if(i < x-1) {
bool phew = 0;
for(int j=0; j<k; j++) phew |= (a[j] > 0);
if(!phew) return 0;
}
}
return 1;
}
long long count_tastiness(long long x, std::vector<long long> a) {
__int128 nxt = -1;
__int128 mul = 1;
__int128 ans = 1;
while(1) {
nxt++;
if(!check(x, nxt * mul, a)) { // find next perfect power, e.g. 6 -> 8
long long lg = 64 - __builtin_clzll(nxt) - 1;
lg = mul * (1ll << (lg + 1));
mul = lg;
// if [0, 9] ok, 10 not ok, ans *= nxt
if(nxt == 1) break;
ans *= nxt;
nxt = 0;
}
}
ans *= nxt;
return ans;
}
