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Description

求一个有$n$个元素的数列，满足任意连续$p$个数的和不小于$s$，任意连续$q$个数的和不大于$t$。

Input

输入包括五个数$n,p,q,s,t(1\le n,p,q \le 500, 1 \le s,t \le 100000)$

Output

如果不能做到，输出"No"

否则输出"Yes"，并在第二行输出一个可行解，包括n个数,保证在$int$范围内有解。

Samples

4 2 2 1 2

Yes
1 0 1 0

Resources

2017 UESTC Training for Graph Theory