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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define N 100020
#define ll long long
using namespace std;
inline int read(){
	int x=0,f=1;char ch=getchar();
	while(ch>'9'||ch<'0')ch=='-'&&(f=0)||(ch=getchar());
	while(ch<='9'&&ch>='0')x=(x<<3)+(x<<1)+ch-'0',ch=getchar();
	return f?x:-x;
}
std::map<int, bool> to1, to2;
int main(int argc, char const *argv[]) {
	int n = read(), m = read();
	while (m --) {
		int x = read(), y = read();
		if (x > y) swap(x, y);
		if (x == 1) to2[y] = 1;
		if (y == n) to1[x] = 1;
	}
	for (int i = 2; i < n; i++)
		if (to1[i] && to2[i])
			return puts("POSSIBLE")&0;
	puts("IMPOSSIBLE");
	return 0;
}