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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)


function checkRegularFlights(i, ns, N, cnt) {
    if (cnt <= 2) {
        var dests = findDestinations(i, ns);
        for (var i = 0; i < dests.length; i++) {
            var dest = dests[i];
            if (dest == N)
                return true;
            if (checkRegularFlights(dest, ns, N, cnt + 1))
                return true;
        }
        function findDestinations(i, ns) {
            for (var n in ns) {
                if (n == i)
                    return ns[n];
            }
            return [];
        }
    }
    return false;
}
function Main(input) {
    var lines = input.split("\n");
    var ns = [];
    var N = -1;
    for (var i = 0; i < lines.length; i++) {
        var line = lines[i];
        var mc = lines[i].match(/(\d+) (\d+)/);
        if (mc) {
            var n = parseInt(mc[1]);
            var m = parseInt(mc[2]);
            if (!(n in ns))
                ns[n] = [];
            ns[n].push(m);
            if (n > N)
                N = n;
        }
    }
    var result = checkRegularFlights(1, ns, N, 1)
        ? "POSSIBLE"
        : "IMPOSSIBLE";
    console.log(result);
}

// ※この行以降は編集しない (標準入力から一度に読み込みMainを呼び出します)
Main(require("fs").readFileSync("/dev/stdin", "utf8"));