#include <bits/stdc++.h>
using namespace std;
#define int long long
const int LIMIT = 60;
map<int,int> right_shift(int x,map<int,int> &inp){
map<int,int> ans;
for(auto[a,b]:inp)ans[a+x]=b;
if(!ans.empty()){
int offset = ans.begin()->second;
ans.erase(ans.begin());
ans[0]=offset;
}
return ans;
}
map<int,int> left_shift(int x,map<int,int> &inp){
map<int,int> ans;
for(auto[a,b]:inp)ans[a-x]=b;
auto iter = ans.begin();
int currsum = 0;
while(iter!=ans.end()){
if(iter->first>=0)break;
currsum+=iter->second;
iter = ans.erase(iter);
}
ans[0]+=currsum;
return ans;
}
void add(map<int,int> &inp1,map<int,int> &inp2){
if(inp1.size()<inp2.size())swap(inp1,inp2);
for(auto[a,b]:inp2){
inp1[a]+=b;
if(inp1[a]==0)inp1.erase(a);
}
}
map<int,int> shift(int x,map<int,int> &inp){
if(x<0)return right_shift(-x,inp);
else if(0<x)return left_shift(x,inp);
return inp;
}
map<int,int> collapse(map<int,int> &inp){
map<int,int> ans;
for(auto[a,b]:inp)ans[(a+1ll)/2ll]+=b;
auto iter = ans.begin();
while(iter!=ans.end()){
if(iter->second==0)iter=ans.erase(iter);
else iter++;
}
return ans;
}
long long count_tastiness(long long x, std::vector<long long> a) {
map<pair<int,int>,long long> memo;
function<long long(long long,long long)> calc = [&](long long i,long long j){
j=max(j,0ll);
if(i==-1)return j==0 ? 1ll : 0ll;
if(j>(((long long)1e18)/(1ll<<i)))return 0ll;
if(memo.count({i,j}))return memo[{i,j}];
long long ac = calc(i-1,2ll*(j-a[i]));
if(ac>0)return memo[{i,j}] = calc(i-1,2ll*(j-a[i]+x))+ac;
else return memo[{i,j}]=0ll;
};
a.resize(LIMIT+1);
map<int,int> curr;
curr[1]=-1;
curr[0]=1;
for(int i=0;i<=LIMIT;i++){
map<int,int> t = shift((-a[i]),curr);
map<int,int> tt = shift((-a[i]+x),curr);
add(t,tt);
curr = collapse(t);
}
return curr[0];
}
