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: Accepted)

/*2019/10/02 */
/*template*/
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<string.h>
#define MOD 1000000007
#define MIN 999999999
#define MAX -999999999
typedef long long int ll;
typedef unsigned long long int ull;
void llswap(ll *x,ll *y){ll tmp;tmp=*x;*x=*y;*y=tmp;}
void swap(int *x,int *y){int tmp;tmp=*x;*x=*y;*y=tmp;}
int rmax(int x,int y){return x>y?x:y;}
int rmin(int x,int y){return x>y?y:x;}
ll llrmax(ll x,ll y){return x>y?x:y;}
ll llrmin(ll x,ll y){return x>y?y:x;}
int asc(const void *a,const void *b){if(*(int*)a < *(int*)b)return -1;else if(*(int*)a == *(int*)b)return 0;else return 1;}
int desc(const void *a,const void *b){if(*(int*)a < *(int*)b)return 1;else if(*(int*)a == *(int*)b)return 0;else return -1;}
int llasc(const void *a,const void *b){if(*(ll*)a < *(ll*)b)return -1;else if(*(ll*)a == *(ll*)b)return 0;else return 1;}
int lldesc(const void *a,const void *b){if(*(ll*)a < *(ll*)b)return 1;else if(*(ll*)a == *(ll*)b)return 0;else return -1;}
int gcd(int x,int y){if(y==0)return x;return gcd(y,x%y);}
 
typedef struct{
    int a;
    int b;
}pair_t;
//int asc_t(const void *a,const void *b){if((pair_t*)a->d < (pair_t*)b->d)return -1;else if((pair_t*)a->d == (pair_t*)b->d)return 0;else return 1;}
int desc_t(const void *a,const void *b){if(((pair_t*)a)->b < ((pair_t*)b)->b)return 1;else if(((pair_t*)a)->b == ((pair_t*)b)->b)return 0;else return -1;}


int main(){
    int n,m;
    pair_t pair[200000]; 

    scanf("%d %d",&n,&m);
    for(int i=0;i<m;i++){
        scanf("%d %d",&pair[i].a,&pair[i].b);
    }

    int rlt[300000]={};
    
    for(int i=0;i<m;i++){
        if(pair[i].b==n){
            rlt[pair[i].a]=n;
        }
    }
    for(int i=0;i<m;i++){
        if(pair[i].a==1){
            if(rlt[pair[i].b]==n){
                printf("POSSIBLE\n");
                return 0;
            }
        }
    }
    printf("IMPOSSIBLE\n");
    return 0;
}