#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;
}
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