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=[list(map(int,input().split())) for i in range(m)]
#print(n,m,l)
def bin_search(a,li):
    max_len=len(li)
    min_len=0
    while max_len>min_len:
        mid=(max_len+min_len)//2
        if li[mid]==a:
            return True
        elif abs(min_len-max_len)==1 and li[mid]!=a:
            break
        elif li[mid]<a:
            min_len=mid
        else:
            max_len=mid
s=[]
g=[]
for i in l:
    if i[0]==1:
        s.append(i[1])
    if i[1]==n:
        g.append(i[0])
g.sort
for i in s:
    if bin_search(i,g):
        print('POSSIBLE')
        break
else:
    print('IMPOSSIBLE')