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#3905. 冰球锦标赛

الإحصائيات

比赛共有来自 $m$ 个国家的 $2 \times n$ 支队伍。这些队伍被随机配对成 $n$ 对。已知两支队伍来自同一个国家的配对数量的期望值。请找出一个符合给定期望值的国家队伍分布方案。

输入格式

输入一行包含两个正整数 $x$ 和 $y$。期望值等于 $\frac{x}{y}$。

$1 \le x, y \le 1000$

输出格式

如果不存在合适的队伍分布方案,输出一行 “-1”。

否则,在第一行输出一个正整数 $m$ —— 参赛国家的数量。在第二行输出 $m$ 个由空格分隔的正整数 —— 每个国家对应的队伍数量。输出的数字之和必须为偶数且不得超过 $10^4$。保证如果存在合适的分布,则一定存在满足上述限制的分布。

样例

样例输入 1

2 1

样例输出 1

1
4

样例输入 2

1 2

样例输出 2

-1

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