Bobo has a graph with n vertices and m edges where the i-th edge is between the vertices and . Find out whether is possible for him to choose some of the edges such that the i-th vertex is incident with exactly edges.

输入描述:

The input consists of several test cases terminated by end-of-file.

The first line of each test case contains two integers n and m.
The second line contains n integers .
The i-th of the following m lines contains two integers  and .

* 
* 
* 
* 
* 
*  for 
* The number of tests does not exceed 100.

输出描述:

For each test case, print "`Yes`" without quotes if it is possible. Otherwise, print "`No`" without quotes.

2 1
1 1
1 2
2 1
2 2
1 2
3 2
1 1 2
1 3
2 3

Yes
No
Yes