Alarm Clocks Everywhere
Contest: Educational Codeforces Round 63 (Rated for Div. 2)
Difficulty rating: 1300
Tags: math, number theory

Ivan is going to sleep now and wants to set his alarm clock. There will be many necessary events tomorrow, the $$$i$$$-th of them will start during the $$$x_i$$$-th minute. Ivan doesn't want to skip any of the events, so he has to set his alarm clock in such a way that it rings during minutes $$$x_1, x_2, \dots, x_n$$$, so he will be awake during each of these minutes (note that it does not matter if his alarm clock will ring during any other minute).

Ivan can choose two properties for the alarm clock — the first minute it will ring (let's denote it as $$$y$$$) and the interval between two consecutive signals (let's denote it by $$$p$$$). After the clock is set, it will ring during minutes $$$y, y + p, y + 2p, y + 3p$$$ and so on.

Ivan can choose any minute as the first one, but he cannot choose any arbitrary value of $$$p$$$. He has to pick it among the given values $$$p_1, p_2, \dots, p_m$$$ (his phone does not support any other options for this setting).

So Ivan has to choose the first minute $$$y$$$ when the alarm clock should start ringing and the interval between two consecutive signals $$$p_j$$$ in such a way that it will ring during all given minutes $$$x_1, x_2, \dots, x_n$$$ (and it does not matter if his alarm clock will ring in any other minutes).

Your task is to tell the first minute $$$y$$$ and the index $$$j$$$ such that if Ivan sets his alarm clock with properties $$$y$$$ and $$$p_j$$$ it will ring during all given minutes $$$x_1, x_2, \dots, x_n$$$ or say that it is impossible to choose such values of the given properties. If there are multiple answers, you can print any.

Input format:
The first line of the input contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 3 \cdot 10^5, 1 \le m \le 3 \cdot 10^5$$$) — the number of events and the number of possible settings for the interval between signals.

The second line of the input contains $$$n$$$ integers $$$x_1, x_2, \dots, x_n$$$ ($$$1 \le x_i \le 10^{18}$$$), where $$$x_i$$$ is the minute when $$$i$$$-th event starts. It is guaranteed that all $$$x_i$$$ are given in increasing order (i. e. the condition $$$x_1 < x_2 < \dots < x_n$$$ holds).

The third line of the input contains $$$m$$$ integers $$$p_1, p_2, \dots, p_m$$$ ($$$1 \le p_j \le 10^{18}$$$), where $$$p_j$$$ is the $$$j$$$-th option for the interval between two consecutive signals.

Output format:
If it's impossible to choose such values $$$y$$$ and $$$j$$$ so all constraints are satisfied, print "NO" in the first line.

Otherwise print "YES" in the first line. Then print two integers $$$y$$$ ($$$1 \le y \le 10^{18}$$$) and $$$j$$$ ($$$1 \le j \le m$$$) in the second line, where $$$y$$$ is the first minute Ivan's alarm clock should start ringing and $$$j$$$ is the index of the option for the interval between two consecutive signals (options are numbered from $$$1$$$ to $$$m$$$ in the order they are given input). These values should be chosen in such a way that the alarm clock will ring during all given minutes $$$x_1, x_2, \dots, x_n$$$. If there are multiple answers, you can print any.

Constraints:
Time limit: 3.0 s
Memory limit: 256.0 MB

Example input:
3 5
3 12 18
2 6 5 3 3

Example output:
YES
3 4

Example input:
4 2
1 5 17 19
4 5

Example output:
NO

Editorial:
It is obvious that we can always take $$$x_1$$$ as $$$y$$$. But we don't know which value of $$$p$$$ we can take. Let $$$d_i$$$ be $$$x_{i + 1} - x_i$$$ for all $$$i$$$ from $$$1$$$ to $$$n-1$$$. The value of $$$p$$$ should be divisor of each value of $$$d_i$$$. The maximum possible divisor of each $$$d_i$$$ is $$$g = gcd(d_1, d_2, \dots, d_{n-1})$$$ (greatest common divisor). And then it is obvious that the value of $$$p$$$ should be the divisor of $$$g$$$. So we have to find any divisor of $$$g$$$ among all values $$$p_j$$$. If there is no such value then the answer is "NO".
Time complexity: $$$O(n \log n)$$$.