#include "coins.h"
using namespace std;
// Arnavaz's move: flip one coin so that the new XOR‐parity equals c
vector<int> coin_flips(vector<int> b, int c) {
int P = 0;
for (int i = 0; i < 64; i++) {
if (b[i]) P ^= i;
}
// flip position
return {P ^ c};
}
// Shahrnaz's move: compute XOR of all tail‐positions to find c
int find_coin(vector<int> b) {
int P = 0;
for (int i = 0; i < 64; i++) {
if (b[i]) P ^= i;
}
return P;
}
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