CF1155C.Alarm Clocks Everywhere

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.

伊万现在准备睡觉，他想设置自己的闹钟。明天将发生许多重要事件，其中第 $i$ 个事件将在第 $x_i$ 分钟开始。伊万不想错过任何事件，因此他必须将闹钟设置成在第 $x_1, x_2, \dots, x_n$ 分钟均响起，从而确保他在每个这样的时刻都处于清醒状态（注意：闹钟在其他任意时刻是否响起并不重要）。

伊万可以为闹钟选择两个参数：第一次响起的时刻（记为 $y$），以及两次连续响铃之间的间隔（记为 $p$）。设定完成后，闹钟将在第 $y,\ y + p,\ y + 2p,\ y + 3p,\ \dots$ 分钟依次响起。

伊万可任选一个分钟作为首次响铃时间 $y$，但他无法任意选择 $p$ 的值；他只能从给定的若干选项 $p_1, p_2, \dots, p_m$ 中挑选（因为他的手机不支持其他取值）。

因此，伊万需选择一个起始时刻 $y$ 和某个间隔 $p_j$，使得闹钟在所有给定时刻 $x_1, x_2, \dots, x_n$ 均会响起（而在其他时刻是否响起无关紧要）。

你的任务是：找出一个起始时刻 $y$ 和对应的下标 $j$，使得当伊万以 $y$ 和 $p_j$ 设置闹钟时，它能在所有给定时刻 $x_1, x_2, \dots, x_n$ 均响起；若不存在满足条件的 $y$ 和 $p_j$，则报告不可能。若存在多个解，输出任意一个即可。

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 $x_1 \lt x_2 \lt \dots \lt x_n$ 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.

输入的第一行包含两个整数 $n$ 和 $m$（$2 \le n \le 3 \cdot 10^5,\ 1 \le m \le 3 \cdot 10^5$）—— 分别表示事件的数量和信号间隔的可能取值数量。

输入的第二行包含 $n$ 个整数 $x_1, x_2, \dots, x_n$（$1 \le x_i \le 10^{18}$），其中 $x_i$ 表示第 $i$ 个事件开始的分钟时刻。保证所有 $x_i$ 按严格递增顺序给出（即满足 $x_1 \lt x_2 \lt \dots \lt x_n$）。

输入的第三行包含 $m$ 个整数 $p_1, p_2, \dots, p_m$（$1 \le p_j \le 10^{18}$），其中 $p_j$ 表示第 $j$ 种信号间隔的候选值。

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.

如果无法选择满足所有约束条件的 $y$ 和 $j$，则在第一行输出 "NO"。

否则，在第一行输出 "YES"；在第二行输出两个整数 $y$（$1 \le y \le 10^{18}$）和 $j$（$1 \le j \le m$），其中 $y$ 表示 Ivan 的闹钟首次响铃的分钟时刻，$j$ 表示所选的连续两次响铃时间间隔选项的编号（选项按输入顺序编号为 $1$ 至 $m$）。所选的 $y$ 和 $j$ 必须保证闹钟在所有给定的时刻 $x_1, x_2, \dots, x_n$ 均会响铃。若存在多个可行解，输出任意一个即可。