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 (2.7.6) (judge verdict: Accepted)

import copy

N, M = map(int, raw_input().split())
dic = {}

for i in range(M):
    tmp = map(int, raw_input().split())
    if tmp[0] not in dic:
        dic[tmp[0]] = []
        dic[tmp[0]].append(tmp[1])
    else:
        dic[tmp[0]].append(tmp[1])
    if tmp[1] not in dic:
        dic[tmp[1]] = []
        dic[tmp[1]].append(tmp[0])
    else:
        dic[tmp[1]].append(tmp[0])

flag = 0

key1 = copy.deepcopy(dic[1])
for i in key1:
    key2 = copy.deepcopy(dic[i])
    for i in key2:
        if i == N:
            flag = 1

if flag == 1:
    print "POSSIBLE"
else:
    print "IMPOSSIBLE"