#include "coins.h"
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx,avx2,fma,popcnt")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
/* DEFINES */
#define S second
#define F first
#define ll long long
#define ull unsigned long long
#define ld long double
#define npos ULLONG_MAX
#define INF LLONG_MAX
#define vv(a) vector<a>
#define ss(a) set<a>
#define pp(a, b) pair<a, b>
#define mm(a, b) map<a, b>
#define qq(a) queue<a>
#define pq(a) priority_queue<a>
#define ump(a, b) unordered_map<a, b>
#define ANDROID \
ios_base::sync_with_stdio(0); \
cin.tie(0); \
cout.tie(0);
#define allc(a) begin(a), end(a)
#define all(a) a, a + sizeof(a) / sizeof(a[0])
#define elif else if
#define endl "\n"
#define pb push_back
#define ins insert
#define logi __lg
#define sqrt sqrtl
#define mpr make_pair
using namespace std;
using namespace __cxx11;
using namespace __gnu_pbds;
typedef char chr;
typedef basic_string<chr> str;
template <typename T, typename key = less<T>>
using ordered_set = tree<T, null_type, key, rb_tree_tag, tree_order_statistics_node_update>;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
std::vector<int> coin_flips(std::vector<int> b, int c) {
std::vector<int> flips(1);
ll xxor = 0;
for (ll i = 0; i < 64; i++)
xxor ^= i * b[i];
flips[0] = xxor ^ c;
return flips;
}
int find_coin(std::vector<int> b) {
ll ans = 0;
for (ll i = 0; i < 64; i++)
ans ^= i * b[i];
return ans;
}
