#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
ll count_tastiness(ll x, vector<ll> a) {
a.resize(128);
vector<pll> c = {{0, 1}};
for (ll i = 0; i < 120; i++) {
vector<pll> nc, ncd;
for (pair<ll, ll> uv : c) {
ll u, v;
tie(u, v) = uv;
u = (u>>1)+a[i];
nc.emplace_back(u, v);
if (u >= x) ncd.emplace_back(u-x, v);
}
int ptrl = 0, ptrr = 0;
vector<pll> nnc;
while (ptrl < nc.size() && ptrr < ncd.size()) {
ll u, v;
if (nc[ptrl].first < ncd[ptrr].first) tie(u, v) = nc[ptrl++];
else tie(u, v) = ncd[ptrr++];
if (nnc.empty() || nnc.back().first != u) nnc.emplace_back(u, v);
else nnc.back().second += v;
}
while (ptrl < nc.size()) {
ll u, v;
tie(u, v) = nc[ptrl++];
if (nnc.empty() || nnc.back().first != u) nnc.emplace_back(u, v);
else nnc.back().second += v;
}
while (ptrr < ncd.size()) {
ll u, v;
tie(u, v) = nc[ptrr++];
if (nnc.empty() || nnc.back().first != u) nnc.emplace_back(u, v);
else nnc.back().second += v;
}
c = nnc;
}
ll ans = 0;
for (auto [u, v] : c) ans += v;
return ans;
}
