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

Example Output

NO
4 2