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Time Limit: 1.0 s Memory Limit: 256 MB Total points: 100 Hackable ✓

#9167. 互质数组

Statistics

给定两个整数 $s$ 和 $x$,请找出一个最短的数组,使得其所有元素的和为 $s$,且所有元素都与 $x$ 互质。

如果两个整数的唯一公约数是 $1$,则称这两个整数互质。

输入格式

输入仅一行,包含两个整数 $s$ 和 $x$ ($2 \le s, x \le 10^9$)。

输出格式

如果不存在满足条件的数组,输出一个整数 $-1$。

否则,第一行输出一个整数 $n$ ($1 \le n \le 10^6$),表示数组的长度。第二行输出 $n$ 个用空格隔开的整数,即该数组本身。数组中的元素绝对值不应超过 $10^9$。

如果存在多个可能的答案,输出任意一个即可。我们已经证明,如果存在解,则一定存在满足上述约束条件的解。

样例

样例输入 1

9 6

样例输出 1

3
-7 -7 23

样例输入 2

14 34

样例输出 2

2
83 -69

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