2024.12.28 周六

Q1. 1100

You are given two integers $l \le r$. You need to find positive integers $a$ and $b$ such that the following conditions are simultaneously satisfied:

• $l \le a + b \le r$
• $\gcd(a, b) \neq 1$

or report that they do not exist.

$\gcd(a, b)$ denotes the greatest common divisor of numbers $a$ and $b$. For example, $\gcd(6, 9) = 3$, $\gcd(8, 9) = 1$, $\gcd(4, 2) = 2$.

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• 一道小数论。

A1.

1. 给定一个区间，是否能找到整数 $a,b$ ，使和在区间内且不互质。
2. 找到最大的偶数 $even$，$n>3$ 时答案可以为：$2,even-2$。若 $even$ 不在区间内只有一种可能 $l=r&&r为奇数$，这种情况仅当 $r$ 是合数有解，找因子。

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A1.

#include <bits/stdc++.h>
#define int long long //
#define endl '\n'     // 交互/调试 关
using namespace std;
#define bug(BUG) cout << "bug:# " << (BUG) << endl
#define bug2(BUG1, BUG2) cout << "bug:# " << (BUG1) << " " << (BUG2) << endl
#define bug3(BUG1, BUG2, BUG3) cout << "bug:# " << (BUG1) << ' ' << (BUG2) << ' ' << (BUG3) << endl
void _();
signed main()
{
    ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    cout << fixed << setprecision(6);
    int T = 1;
    cin >> T;
    while (T--)
        _();
    return 0;
}
void _()
{
    int l, r;
    cin >> l >> r;
    int a = 2;
    int max_even = r & 1 ? r - 1 : r;
    int b = max_even - 2;
    if (b < 2)
    {
        cout << -1 << endl;
        return;
    }
    if (l == r && (r & 1))
    {
        for (int i = 2; i <= r / i; i++)
            if (r % i == 0)
            {
                int k = r / i;
                cout << i << ' ' << (k - 1) * i << endl;
                return;
            }
        cout << -1 << endl;
        return;
    }
    cout << a << " " << b << endl;
}