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>
#include <type_traits>
using namespace std;

using ll = int64_t;
#define int ll

#define FOR(i, a, b) for (int i = int(a); i < int(b); i++)
#define REP(i, b) FOR(i, 0, b)
#define MP make_pair
#define PB push_back
#define EB emplace_back
#define ALL(x) x.begin(), x.end()

using pi = pair<int, int>;
using vi = vector<int>;
using ld = long double;

template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << "(" << p.first << "," << p.second << ")";
  return os;
}

template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
  os << "{";
  REP(i, (int)v.size()) {
    if (i)
      os << ",";
    os << v[i];
  }
  os << "}";
  return os;
}

ll read() {
  ll i;
  scanf("%" SCNd64, &i);
  return i;
}

void printSpace() { printf(" "); }

void printEoln() { printf("\n"); }

void print(ll x, int suc = 1) {
  printf("%" PRId64, x);
  if (suc == 1)
    printEoln();
  if (suc == 2)
    printSpace();
}

string readString() {
  static char buf[3341000];
  scanf("%s", buf);
  return string(buf);
}

char *readCharArray() {
  static char buf[3341000];
  static int bufUsed = 0;
  char *ret = buf + bufUsed;
  scanf("%s", ret);
  bufUsed += strlen(ret) + 1;
  return ret;
}

template <class T, class U> void chmax(T &a, U b) {
  if (a < b)
    a = b;
}

template <class T, class U> void chmin(T &a, U b) {
  if (b < a)
    a = b;
}

template <class T> T Sq(const T &t) { return t * t; }

const int mod = 1e9 + 7;

signed main() {
  int n, m;
  std::cin >> n >> m;
  vi fromTo;
  vector<bool> canGo(n + 1);
  REP(i, m) {
    int a = read(), b = read();
    if (a == 1)
      fromTo.PB(b);
    if (b == n)
      canGo[a] = true;
  }
  bool ok = false;
  for (auto &v : fromTo)
    if (canGo[v])
      ok = true;
  if (ok)
    std::cout << "POSSIBLE" << std::endl;
  else
    std::cout << "IMPOSSIBLE" << std::endl;
}