You have two IP cameras of the same model. Each camera can take photos starting from some moment of time with a fixed period. You can freely choose the starting moment but you can choose the period only as one of k values p_1, p_2, ..., p_k which are chosen by the camera's manufacturer.

You have n moments of interest x_1, x_2, ..., x_n. You'd like to configure both cameras in such a way that at least one camera will take a photo in each of these moments. Configuring the camera means setting the moment when it takes the first photo and the gap between two consecutive photos (which should be one of the values p_1, p_2, ..., p_k). It's not a problem for you that cameras can take photos at other moments of time — you only care about moments of interest.

Input

The first line contains two integers k and n (1 ≤ k ≤ 10^5; 2 ≤ n ≤ 10^5) — the number of periods to choose and the number of moments of interest.

The second line contains k integers p_1, p_2, ..., p_k (1 ≤ p_1 < p_2 < ... < p_k ≤ 10^6) — the periods to choose in the ascending order.

The third line contains n integers x_1, x_2, ..., x_n (1 ≤ x_1 < x_2 < ... < x_n ≤ 10^6) — the moments of interest in the ascending order.

Output

Print YES (case insensitive) in the first line if there is a way to configure cameras.

In the second line, print two integers s_1 and cp_1 (1 ≤ s_1 ≤ 10^6; 1 ≤ cp_1 ≤ 10^6; cp_1 ∈ \\{p_1, ..., p_k\}) — the starting moment and the period for the first camera. The period should be one of the given periods.

In the third line, print two integers s_2 and cp_2 (1 ≤ s_2 ≤ 10^6; 1 ≤ cp_2 ≤ 10^6; cp_2 ∈ \\{p_1, ..., p_k\}) — the starting moment and the period for the second camera. The period should be one of the given periods.

If there is no way to configure cameras, print NO (case insensitive). If there are multiple ways, you may print any of them.

Examples

Input


3 5
3 5 7
1 4 5 7 12


Output


YES
1 3
5 7


Input


3 2
1 2 3
1 10


Output


YES
1 1
10 1


Input


3 4
1 2 3
5 7 9 11


Output


YES
5 1
5 1


Input


3 4
10 20 100
2 3 4 7


Output


NO

Source: codeforces | Difficulty: HARD
Tags: Number theory

Mathematics


Solutions: