There are n cities and m flight connections. Your task is to check if you can travel from any city to any other city using the available flights.

Input

The first input line has two integers n and m: the number of cities and flights. The cities are numbered 1,2,\dots,n.

After this, there are m lines describing the flights. Each line has two integers a and b: there is a flight from city a to city b. All flights are one-way flights.

Output

Print "YES" if all routes are possible, and "NO" otherwise. In the latter case also print two cities a and b such that you cannot travel from city a to city b. If there are several possible solutions, you can print any of them.

Constraints

• 1 \le n \le 10^5
• 1 \le m \le 2 \cdot 10^5
• 1 \le a,b \le n

Example

Input:

4 5
1 2
2 3
3 1
1 4
3 4

Output:

NO
4 2