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 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
#include <cmath>
#include <queue>
#include <stack>
#include <deque>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <tuple>
#include <numeric>
#include <string>
#include <bitset>
#include <functional>

using ld = long double;
using vld = std::vector<ld>;
using vvld = std::vector<vld>;
using vvvld = std::vector<vvld>;
using ll = long long;
using vll = std::vector<ll>;
using vvll = std::vector<vll>;
using vvvll = std::vector<vvll>;
using pll = std::pair<ll, ll>;
using vpll = std::vector<pll>;
using str = std::string;
using vstr = std::vector<str>;

template<typename T> bool chmin(T a, T &b) { return a < b ? b = a, true : false; }
template<typename T> bool chmax(T a, T &b) { return a > b ? b = a, true : false; }

constexpr ld PI = 3.141592653589793L;
constexpr ld EPS = std::numeric_limits<ld>::epsilon();

ll gcd(ll n, ll m) { return m ? gcd(m, n % m) : n; }
ll lcm(ll n, ll m) { return n / gcd(n, m) * m; }
bool isprime(ll n) {
    if (n < 2) return false;
    for (ll i = 2; i * i <= n; i++)
        if (n % i == 0) return false;
    return true;
}
ll rpow(ll x, ll n) {
    if (n == 0) return 1;
    ll k = 1;
    for (; n > 1; n /= 2) {
        if (n & 1) k *= x;
        x *= x;
    }
    return k * x;
}
ll modpow(ll x, ll n, ll mod) {
    if (n == 0) return 1;
    ll k = 1;
    for (; n > 1; n /= 2) {
        if (n & 1) (k *= x) %= mod;
        (x *= x) %= mod;
    }
    return k * x % mod;
}
ll modcomb(ll n, ll r, ll mod) {
    if (r < 0 || n < r) return 0;
    chmin(n - r, r);
    ll mul = 1, div = 1;
    for (ll i = 0; i < r; i++) {
        (mul *= n - i) %= mod;
        (div *= i + 1) %= mod;
    }
    return mul * modpow(div, mod - 2, mod) % mod;
}

/*------------------------------------------------------------------------*/

void solve();

int main() {
    std::cin.tie(0);
    std::ios::sync_with_stdio(false);
    std::cout << std::setprecision(15);

    solve();
}
void solve() {
    ll n, m;
    std::cin >> n >> m;

    vvll island(n);
    for (ll i = 0; i < m; i++) {
        ll a, b; std::cin >> a >> b;
        a--, b--;
        island[a].push_back(b);
        island[b].push_back(a);
    }

    auto bfs = [&]() -> ll {
        vll dist(n, -1); dist[0] = 0;
        std::queue<ll> que; que.push(0);

        while (!que.empty()) {
            ll cur = que.front(); que.pop();
            for (ll next : island[cur])
                if (dist[next] == -1) {
                    dist[next] = dist[cur] + 1;
                    que.push(next);
                }
        }

        return dist[n - 1];
    };

    std::cout << (bfs() == 2 ? "POSSIBLE" : "IMPOSSIBLE") << '\n';
}