Problem:
Score : 300 points

Problem Statement

In Takahashi Kingdom, there is an archipelago of N islands, called Takahashi Islands.
For convenience, we will call them Island 1, Island 2, ..., Island N.

There are M kinds of regular boat services between these islands.
Each service connects two islands. The i-th service connects Island a_i and Island b_i.

Cat Snuke is on Island 1 now, and wants to go to Island N.
However, it turned out that there is no boat service from Island 1 to Island N, so he wants to know whether it is possible to go to Island N by using two boat services.

Help him.

Constraints

3 ≤ N ≤ 200 000

1 ≤ M ≤ 200 000

1 ≤ a_i < b_i ≤ N

(a_i, b_i) \neq (1, N)

If i \neq j, (a_i, b_i) \neq (a_j, b_j).

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

If it is possible to go to Island N by using two boat services, print POSSIBLE; otherwise, print IMPOSSIBLE.

Sample Input 1

3 2
1 2
2 3

Sample Output 1

POSSIBLE

Sample Input 2

4 3
1 2
2 3
3 4

Sample Output 2

IMPOSSIBLE

You have to use three boat services to get to Island 4.

Sample Input 3

100000 1
1 99999

Sample Output 3

IMPOSSIBLE

Sample Input 4

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

Sample Output 4

POSSIBLE

You can get to Island 5 by using two boat services: Island 1 -> Island 4 -> Island 5.

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

N , M = map(int, input().split())

L=[[0]*2 for i in range(M)]

for i in range(M):
    L[i][0] , L[i][1] = map(int, input().split())

A=[10**10]*M
B=[10**10]*M

L=sorted(L ,key=lambda x: x[0])

for i in range(M):
    if L[i][0] == 1:
        A[i]=L[i][1]
    else:
        break

L=sorted(L ,key=lambda x: -x[1])

for i in range(M):
    if L[i][1] == N:
        B[i]=L[i][0]
    else:
        break

for i in A:
    for j in B:
        if i == j:
            print("POSSIBLE")
            exit()
        if j == 10**10 : break
    if i == 10**10 : 
        print("IMPOSSIBLE")
        exit()