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>
using namespace std;
using ll = long long;
#define int ll
#define rep(i,n) for(int i=0;i<n;i++)
#define all(in) in.begin(), in.end()
constexpr int INF = (numeric_limits<int>::max() == INT_MAX ? (int)1e9 : (long long)1e18);
constexpr long double eps = 1e-6;
const string el = "\n";
template<class T, class S> void cmin(T &a, const S &b) { if (a > b)a = b; }
template<class T, class S> void cmax(T &a, const S &b) { if (a < b)a = b; }
template<typename Head, typename Value> auto vectors(const Head &head, const Value &v) { return vector<Value>(head, v); }
template<typename Head, typename... Tail> auto vectors(Head x, Tail... tail) { auto inner = vectors(tail...); return vector<decltype(inner)>(x, inner); }
using ld  = long double;using pii = pair<int,int>;using piii = pair<int,pii>;
int W,H;
int dx[]={0,0,1,-1}, dy[]={1,-1,0,0};
bool valid(int x,int y){return (0<=x&&x<W)&&(0<=y&&y<H);}
void fast_io(){ios::sync_with_stdio(false); cin.tie(nullptr);}
template<class T> T gcd(T a,  T b) {return b ? gcd(b, a % b) : a;}
template<class U> U lcm( U m, U n ){if((0 == m )||( 0 == n ))return 0; return ((m / gcd(m, n)) * n); }
bool j = false;
int n;
void dfs(int v,int d,vector<vector<int>>&edge){
    if(d == 2){
        if(v == n - 1) j = true;
        return;
    }
    for(auto nv : edge[v]){
        if(nv == v) continue;
        dfs(nv,d + 1, edge);
    }
}
signed main(){
    fast_io();
    int m; cin >> n >> m;
    vector<vector<int>>edge(n);
    rep(i,m){
        int a,b; cin >> a >> b;
        --a,--b; edge[a].push_back(b);
        edge[b].push_back(a);
    }
    dfs(0,0,edge);
    cout << (j ? "POSSIBLE" : "IMPOSSIBLE") << endl;
}