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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>

int partition(int a [], int l, int r) {
    int i = l - 1;
    int j = r;
    int temp;
 
    int pivot = a[r];
 
    while (1) {
        while (a[++i] < pivot) ;
        while (i < --j && pivot < a[j]) ;

        if (i >= j) break;
 
        temp = a[i];
        a[i] = a[j];
        a[j] = temp;
    }
    temp = a[i];
    a[i] = a[r];
    a[r] = temp;
    return i;
}

void quickSort(int a[], int l, int r) {
    int v;
    if (l >= r) {
        return;
    }
    v = partition(a, l, r);
    quickSort(a, l, v - 1);
    quickSort(a, v + 1, r);
}

int main() {
	int N, M;
	scanf("%d %d", &N, &M);
	int a[N], b[N], s, t, k = 0, l = 0;
	for (int i = 0; i < M; i++) {
		scanf("%d %d", &s, &t);
		if (s == 1) {
			a[k] = t;
			k++;
		} else if (t == N) {
			b[l] = s;
			l++;
		}
	}
	quickSort(a, 0, k);
	quickSort(b, 0, l);
	s = 0, t = 0;
	while (1) {
	    if (s >= k || t >= l) {
	    	printf("IMPOSSIBLE");
	    	return 0;
	    }
		if (a[s] == b[t]) {
			printf("POSSIBLE");
			return 0;
		} else if (a[s] > b[t]) {
			t++;
		} else {
			s++;
		}
	}
}