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OI-codes/S2OJ/1152/1152.cpp

101 lines
2.8 KiB
C++

#include <iostream>
#include <algorithm>
#include <functional>
#include <iterator>
#include <vector>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 1e5 + 5;
const int mod = 1e9 + 7;
int n, a, b, winner,
cnt_le_a, cnt_le_b, cnt_le_2a, cnt_rest,
ans_winner, ans_first, ans_second;
int fac[N], inv[N], fac_inv[N];
std::vector<int> v;
enum Winner {
Alice = 0,
Bob = 1,
};
int C(int n, int m) {
if (n < m || n < 0 || m < 0) return 0;
return static_cast<long long>(fac[n]) * fac_inv[m] % mod * fac_inv[n - m] % mod;
}
constexpr int binpow(int a, int b, int mod = ::mod) {
int res = 1;
a %= mod;
while (b) {
if (b & 1) res = static_cast<long long>(res) * a % mod;
a = static_cast<long long>(a) * a % mod;
b >>= 1;
}
return res;
}
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
fac[0] = 1;
for (int i = 1; i < N; i++) {
fac[i] = static_cast<long long>(fac[i - 1]) * i % mod;
}
inv[0] = inv[1] = 1;
for (int i = 2; i < N; i++) {
inv[i] = static_cast<long long>(mod - (mod / i)) * inv[mod % i] % mod;
}
fac_inv[0] = fac_inv[1] = 1;
for (int i = 2; i < N; i++) {
fac_inv[i] = static_cast<long long>(fac_inv[i - 1]) * inv[i] % mod;
}
cin >> n >> a >> b;
if (a < b) {
winner = Winner::Alice;
} else {
std::swap(a, b);
winner = Winner::Bob;
}
std::copy_n(std::istream_iterator<int>(cin), n, std::back_inserter(v));
std::transform(v.begin(), v.end(), v.begin(), std::bind(std::modulus<int>(), std::placeholders::_1, a + b));
std::for_each(v.begin(), v.end(), [&](int x) {
if (x < a) cnt_le_a++; // [1, a)
else if (x < b) cnt_le_b++; // [a, b)
else if (x < 2 * a) cnt_le_2a++; // [b, 2a)
else cnt_rest++; // [2a, a + b)
});
for (int i = 0; i <= cnt_le_2a; i++) {
if (i % 2 == 0) {
ans_first = (static_cast<long long>(ans_first) + static_cast<long long>(C(cnt_le_2a, i)) * cnt_rest % mod) % mod;
ans_second = (static_cast<long long>(ans_second) + C(cnt_le_2a, i)) % mod;
} else { // i % 2 == 1
ans_first = (static_cast<long long>(ans_first) + C(cnt_le_2a, i)) % mod;
}
}
ans_first = static_cast<long long>(ans_first) * binpow(2, cnt_le_a) % mod;
ans_second = static_cast<long long>(ans_second) * binpow(2, cnt_le_a) % mod;
ans_winner = ((static_cast<long long>(binpow(2, n)) - ans_first - ans_second) % mod + mod) % mod;
if (winner == Winner::Alice) {
cout << ans_winner << ' ' << 0 << ' ' << ans_first << ' ' << ans_second << endl;
} else {
cout << 0 << ' ' << ans_winner << ' ' << ans_first << ' ' << ans_second << endl;
}
return 0;
}