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: Wrong Answer)

#include<stdio.h>
#include<iostream>
#include<string.h>
#include<algorithm>
#include<map>
#include<vector>
#include<string>
#define ll long long
#define For(i,x,y)  for(ll i=x;i<=y;++i)
#define FOr(i,x,y)  for(ll i=x;i>=y;--i)
using namespace std;
inline ll read(){   ll x=0,f=1;char ch=getchar();   while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}  while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}  return x*f; } 
inline void write(ll x){    if (x<0) putchar('-'),x=-x; if (x>=10) write(x/10);   putchar(x%10+'0');  } 
inline void writeln(ll x){ write(x);   puts("");   }
const ll N=400010;
ll mark[N],head[N],nxt[N],vet[N],m,n,tot;
int main(){
	n=read();	m=read();	mark[1]=1;
	For(i,1,m){
		ll x=read(),y=read();
		if (x==1)	mark[y]=1;
		if (y==n&&mark[x])	return puts("POSSIBLE"),0;
	}puts("IMPOSSIBLE");
}