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)

///////////////////////////////////////////// Template /////////////////////////////////////////////
#![allow(non_snake_case, unused)]
use std::collections::*;

//////////////////// missing functions in 1.15.1 ////////////////////
macro_rules! eprint {
	($($t:tt)*) => { {
		use ::std::io::Write;
		let _ = write!(::std::io::stderr(), $($t)*);
	} };
}
macro_rules! eprintln {
	($($t:tt)*) => { {
		use ::std::io::Write;
		let _ = writeln!(::std::io::stderr(), $($t)*);
	} };
}

//////////////////// useful functions ////////////////////
pub trait SetMin {
	fn setmin(&mut self, v: Self) -> bool;
}
impl<T> SetMin for T where T: PartialOrd {
	fn setmin(&mut self, v: T) -> bool {
		*self > v && { *self = v; true }
	}
}
pub trait SetMax {
	fn setmax(&mut self, v: Self) -> bool;
}
impl<T> SetMax for T where T: PartialOrd {
	fn setmax(&mut self, v: T) -> bool {
		*self < v && { *self = v; true }
	}
}

macro_rules! debug {
	($($v: expr),*) => {
		$(eprint!("{} = {:?} ", stringify!($v), $v);)*
		eprintln!("@ {}:{}", file!(), line!());
	}
}

macro_rules! mat {
	($($e:expr),*) => { Vec::from(vec![$($e),*]) };
	($($e:expr,)*) => { Vec::from(vec![$($e),*]) };
	($e:expr; $d:expr) => { Vec::from(vec![$e; $d]) };
	($e:expr; $d:expr $(; $ds:expr)+) => { Vec::from(vec![mat![$e $(; $ds)*]; $d]) };
}

pub fn readln() -> String {
	let mut line = String::new();
	::std::io::stdin().read_line(&mut line).unwrap_or_else(|e| panic!("{}", e));
	line
}

macro_rules! read {
	($($t:tt),*; $n:expr) => {{
		let stdin = ::std::io::stdin();
		let ret = ::std::io::BufRead::lines(stdin.lock()).take($n).map(|line| {
			let line = line.unwrap();
			let mut it = line.split_whitespace();
			_read!(it; $($t),*)
		}).collect::<Vec<_>>();
		ret
	}};
	($($t:tt),*) => {{
		let line = readln();
		let mut it = line.split_whitespace();
		_read!(it; $($t),*)
	}};
}

macro_rules! _read {
	($it:ident; [char]) => {
		_read!($it; String).chars().collect::<Vec<_>>()
	};
	($it:ident; [u8]) => {
		Vec::from(_read!($it; String).into_bytes())
	};
	($it:ident; [$t:ty]) => {
		$it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::<Vec<_>>()
	};
	($it:ident; $t:ty) => {
		$it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<$t>().unwrap_or_else(|e| panic!("{}", e))
	};
	($it:ident; $($t:ty),+) => {
		($(_read!($it; $t)),*)
	};
}

pub fn main() {
	let _ = ::std::thread::Builder::new().name("run".to_string()).stack_size(32 * 1024 * 1024).spawn(run).unwrap().join();
}
////////////////////////////////////////////////////////////////////////////////////////////////////

fn run() {
	let (N, M) = read!(usize, usize);
	let mut from = vec![false; N];
	let mut to = vec![false; N];
	for (a, b) in read!(usize, usize; M) {
		if a == 1 {
			to[b - 1] = true;
		}
		if b == N {
			from[a - 1] = true;
		}
	}
	if from.into_iter().zip(to.into_iter()).any(|(a, b)| a && b) {
		println!("POSSIBLE");
	} else {
		println!("IMPOSSIBLE");
	}
}