CSES - Flight Routes Check
  • Time limit: 1.00 s
  • Memory limit: 512 MB
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 $b$.

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