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)

# 10 5
# 1 2
# 1 3
# 1 4
# 8 10
# 1 8

n, m = map(int, input().split())

ends = []
starts = []
possible = False
for i in range(m):
    a, b = map(int, input().split())
    if a == 1:
        starts.append([a, b])
    elif b == n:
        ends.append([a, b])

starts.sort(key=lambda x: x[1])
ends.sort(key=lambda x: x[0])
if not (starts and ends):
    print("IMPOSSIBLE")
    import sys
    sys.exit()




i = 0
j = 0
while i != len(starts) and j != len(ends):
    to = starts[i][1]
    fr = ends[j][0]

    if to == fr:
        possible = True
        break

    if to > fr:
        i += 1
    elif fr > to:
        j += 1

while j != len(ends):
    fr = ends[j][0]
    if to == fr:
        possible = True
        break

    j += 1

while i != len(starts):
    to = starts[i][1]
    if to == fr:
        possible = True
        break

    i += 1

print("POSSIBLE") if possible else print("IMPOSSIBLE")