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auto sieve(auto n, auto&& pri, auto&& np) {
    np.resize(n + 1);
    for (auto i = 2; i <= n; i ++) {
        if (not np[i]) pri.push_back(i);
        for (auto j : pri) {
            if (i * j > n) break;
            np[i * j] = true;
            if (i % j == 0) break;
        }
    }
}

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auto pow(auto a, auto b, auto p) {
    auto res = 1;
    for (; b; b /= 2, a = 1ll * a * a % p)
        if (b % 2)
            res = 1ll * res * a % p;
    return res;
}

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auto facted(size_t n) {
    vector<size_t> res;
    for (size_t i = 2; i * i <= n; i++) {
        while (n % i == 0) {
            res.emplace_back(i);
            n /= i;
        }
    }
    if (n > 1)
        res.emplace_back(n);
    return res;
}