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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::{Read, Write};

struct CustomIO<'a> {
    sin: ::std::io::Bytes<::std::io::StdinLock<'a>>,
    sout: ::std::io::StdoutLock<'a>,
    buf: [u8; 20],
}
impl<'a> CustomIO<'a> {
    pub fn new(
        sin: ::std::io::Bytes<::std::io::StdinLock<'a>>,
        sout: ::std::io::StdoutLock<'a>,
    ) -> Self {
        CustomIO::<'a> {
            sin: sin,
            sout: sout,
            buf: [0u8; 20],
        }
    }

    pub fn readu32(&mut self) -> u32 {
        self.sin
            .by_ref()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .fold(0u32, |a, x| a * 10 + (x as u8 - b'0') as u32)
    }

    pub fn readu64(&mut self) -> u64 {
        self.sin
            .by_ref()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .fold(0u64, |a, x| a * 10 + (x as u8 - b'0') as u64)
    }

    pub fn readusize(&mut self) -> usize {
        self.sin
            .by_ref()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .fold(0usize, |a, x| a * 10 + (x as u8 - b'0') as usize)
    }

    pub fn writeu32(&mut self, mut v: u32) {
        let mut i = 20usize;
        while v != 0u32 {
            i -= 1usize;
            self.buf[i] = (v % 10) as u8 + b'0';
            v /= 10;
        }
        if i == 20usize {
            i = 19usize;
            self.buf[19] = b'0';
        }
        let _ = self.sout.write(&self.buf[i..20]);
    }

    pub fn writeu64(&mut self, mut v: u64) {
        let mut i = 20usize;
        while v != 0u64 {
            i -= 1usize;
            self.buf[i] = (v % 10) as u8 + b'0';
            v /= 10;
        }
        if i == 20usize {
            i = 19usize;
            self.buf[19] = b'0';
        }
        let _ = self.sout.write(&self.buf[i..20]);
    }

    pub fn writeusize(&mut self, mut v: usize) {
        let mut i = 20usize;
        while v != 0usize {
            i -= 1usize;
            self.buf[i] = (v % 10) as u8 + b'0';
            v /= 10;
        }
        if i == 20usize {
            i = 19usize;
            self.buf[19] = b'0';
        }
        let _ = self.sout.write(&self.buf[i..20]);
    }
}

fn main() {
    let stdin = ::std::io::stdin();
    let stdout = ::std::io::stdout();
    let mut cio = CustomIO::new(stdin.lock().bytes(),stdout.lock());

    let n= cio.readusize();
    let m= cio.readusize();
    let mut from1 = vec![false; n + 1];
    let mut fromn = vec![false; n + 1];
    for _ in 0..m {
        let a= cio.readusize();
        let b= cio.readusize();
        from1[b] |= a == 1;
        from1[a] |= b == 1;
        fromn[b] |= a == n;
        fromn[a] |= b == n;
    }
    let flg = from1
        .iter()
        .zip(fromn.iter())
        .fold(false, |acc, (&a, &b)| acc || a && b);
    println!("{}", if flg { "POSSIBLE" } else { "IMPOSSIBLE" });
}