Problem:
Score : 300 points

Problem Statement

We have N ID cards, and there are M gates.

We can pass the i-th gate if we have one of the following ID cards: the L_i-th, (L_i+1)-th, ..., and R_i-th ID cards.

How many of the ID cards allow us to pass all the gates alone?

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq L_i \leq R_i \leq N

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1
L_2 R_2
\vdots
L_M R_M

Output

Print the number of ID cards that allow us to pass all the gates alone.

Sample Input 1

4 2
1 3
2 4

Sample Output 1

2

Two ID cards allow us to pass all the gates alone, as follows:

The first ID card does not allow us to pass the second gate.

The second ID card allows us to pass all the gates.

The third ID card allows us to pass all the gates.

The fourth ID card does not allow us to pass the first gate.

Sample Input 2

10 3
3 6
5 7
6 9

Sample Output 2

1

Sample Input 3

100000 1
1 100000

Sample Output 3

100000

Solution in Rust (1.15.1) (judge verdict: Accepted)

// The main code is at the very bottom.

#[allow(unused_imports)]
#[macro_use]
pub mod spella {
  pub mod byte {
    pub use self::byte_char::*;
    pub use self::byte_str::*;
    pub use self::byte_string::*;
    pub use self::from_byte_str::*;

    mod byte_char {
      use std::fmt::{self, Debug, Display, Formatter};

      #[derive(Clone, Copy, Default, PartialEq, Eq, PartialOrd, Ord, Hash)]
      pub struct ByteChar(u8);

      impl ByteChar {
        pub fn new(c: u8) -> Self {
          ByteChar(c)
        }

        pub fn into_byte(self) -> u8 {
          self.0
        }
      }

      impl Debug for ByteChar {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          write!(f, "b'{}'", self.0 as char)
        }
      }

      impl Display for ByteChar {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          write!(f, "{}", self.0 as char)
        }
      }
    }

    mod byte_str {
      use spella::byte::{ByteChar, ByteString};

      use std::fmt::{self, Debug, Display, Formatter};
      use std::ops::{Deref, DerefMut};

      #[derive(PartialEq, Eq, PartialOrd, Ord, Hash)]
      pub struct ByteStr([ByteChar]);

      macro_rules! cast {
        (mut $x:expr, $($T:ty)=>*) => {
          unsafe { &mut *($x $(as *mut $T)*) }
        };
        ($x:expr, $($T:ty)=>*) => {
          unsafe { &*($x $(as *const $T)*) }
        };
      }

      impl ByteStr {
        pub fn from_bytes(s: &[u8]) -> &Self {
          cast!(s, [u8] => [ByteChar] => ByteStr)
        }

        pub fn from_bytes_mut(s: &mut [u8]) -> &mut Self {
          cast!(mut s, [u8] => [ByteChar] => ByteStr)
        }

        pub fn from_byte_chars(s: &[ByteChar]) -> &Self {
          cast!(s, [ByteChar] => ByteStr)
        }

        pub fn from_byte_chars_mut(s: &mut [ByteChar]) -> &mut Self {
          cast!(mut s, [ByteChar] => ByteStr)
        }

        pub fn as_bytes(&self) -> &[u8] {
          cast!(self, ByteStr => [ByteChar] => [u8])
        }

        pub fn as_bytes_mut(&mut self) -> &mut [u8] {
          cast!(mut self, ByteStr => [ByteChar] => [u8])
        }
      }

      impl ToOwned for ByteStr {
        type Owned = ByteString;

        fn to_owned(&self) -> ByteString {
          ByteString::from(self.0.to_owned())
        }
      }

      impl Debug for ByteStr {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          write!(f, "b\"")?;

          for &c in &self.0 {
            write!(f, "{}", c)?;
          }

          write!(f, "\"")
        }
      }

      impl Display for ByteStr {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          for &c in &self.0 {
            write!(f, "{}", c)?;
          }

          Ok(())
        }
      }

      impl Deref for ByteStr {
        type Target = [ByteChar];

        fn deref(&self) -> &[ByteChar] {
          &self.0
        }
      }

      impl DerefMut for ByteStr {
        fn deref_mut(&mut self) -> &mut [ByteChar] {
          &mut self.0
        }
      }
    }

    mod byte_string {
      use spella::byte::{ByteChar, ByteStr};

      use std::borrow::{Borrow, BorrowMut};
      use std::fmt::{self, Debug, Display, Formatter};
      use std::ops::{Deref, DerefMut};

      #[derive(Clone, Default, PartialEq, Eq, PartialOrd, Ord, Hash)]
      pub struct ByteString(Vec<ByteChar>);

      impl ByteString {
        pub fn into_byte_chars(self) -> Vec<ByteChar> {
          self.0
        }

        pub fn as_byte_str(&self) -> &ByteStr {
          ByteStr::from_byte_chars(&self.0)
        }

        pub fn as_mut_byte_str(&mut self) -> &mut ByteStr {
          ByteStr::from_byte_chars_mut(&mut self.0)
        }
      }

      impl From<Vec<ByteChar>> for ByteString {
        fn from(s: Vec<ByteChar>) -> ByteString {
          ByteString(s)
        }
      }

      impl Borrow<ByteStr> for ByteString {
        fn borrow(&self) -> &ByteStr {
          self.as_byte_str()
        }
      }

      impl BorrowMut<ByteStr> for ByteString {
        fn borrow_mut(&mut self) -> &mut ByteStr {
          self.as_mut_byte_str()
        }
      }

      impl Debug for ByteString {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          Debug::fmt(self.as_byte_str(), f)
        }
      }

      impl Display for ByteString {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          Display::fmt(self.as_byte_str(), f)
        }
      }

      impl Deref for ByteString {
        type Target = ByteStr;

        fn deref(&self) -> &ByteStr {
          ByteStr::from_byte_chars(&self.0)
        }
      }

      impl DerefMut for ByteString {
        fn deref_mut(&mut self) -> &mut ByteStr {
          ByteStr::from_byte_chars_mut(&mut self.0)
        }
      }
    }

    mod from_byte_str {
      use spella::byte::{ByteChar, ByteStr, ByteString};

      use std::error::Error;
      use std::fmt::{self, Debug, Display, Formatter};
      use std::str::{self, FromStr, Utf8Error};

      pub trait FromByteStr: Sized {
        type Err;

        fn from_byte_str(s: &ByteStr) -> Result<Self, Self::Err>;
      }

      macro_rules! fn_description {
        () => {
          fn description(&self) -> &str {
            "description() is deprecated; use Display"
          }
        };
      }

      #[derive(Debug)]
      pub struct ParseByteCharError(ParseByteCharErrorKind);

      #[derive(Debug)]
      enum ParseByteCharErrorKind {
        EmptyByteStr,
        TooManyByteChars,
      }

      impl Display for ParseByteCharError {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          use self::ParseByteCharErrorKind::*;

          f.write_str(match self.0 {
            EmptyByteStr => "empty `ByteStr`",
            TooManyByteChars => "too many `ByteChar`s",
          })
        }
      }

      impl Error for ParseByteCharError {
        fn_description! {}
      }

      impl FromByteStr for ByteChar {
        type Err = ParseByteCharError;

        fn from_byte_str(s: &ByteStr) -> Result<Self, Self::Err> {
          use self::ParseByteCharErrorKind::*;

          match s.len() {
            1 => Ok(unsafe { *s.get_unchecked(0) }),
            0 => Err(ParseByteCharError(EmptyByteStr)),
            _ => Err(ParseByteCharError(TooManyByteChars)),
          }
        }
      }

      #[derive(Debug)]
      pub enum ParseByteStringError {}

      impl Display for ParseByteStringError {
        fn fmt(&self, _: &mut Formatter) -> fmt::Result {
          match *self {}
        }
      }

      impl Error for ParseByteStringError {
        fn_description! {}
      }

      impl FromByteStr for ByteString {
        type Err = ParseByteStringError;

        fn from_byte_str(s: &ByteStr) -> Result<Self, Self::Err> {
          Ok(ByteString::from(s.to_vec()))
        }
      }

      pub struct ParseFromStrError<T: FromStr>(ParseFromStrErrorKind<T>);

      enum ParseFromStrErrorKind<T: FromStr> {
        Utf8Error(Utf8Error),
        FromStrError(T::Err),
      }

      impl<T: FromStr> Debug for ParseFromStrError<T>
      where
        T::Err: Debug,
      {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          use self::ParseFromStrErrorKind::*;

          match self.0 {
            Utf8Error(ref err) => f.debug_tuple("Utf8Error").field(err).finish(),
            FromStrError(ref err) => f.debug_tuple("FromStrError").field(err).finish(),
          }
        }
      }

      impl<T: FromStr> Display for ParseFromStrError<T>
      where
        T::Err: Display,
      {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          use self::ParseFromStrErrorKind::*;

          match self.0 {
            Utf8Error(ref err) => write!(f, "{}", err),
            FromStrError(ref err) => write!(f, "{}", err),
          }
        }
      }

      impl<T: FromStr> Error for ParseFromStrError<T>
      where
        T::Err: Debug + Display,
      {
        fn_description! {}
      }

      impl<T: FromStr> FromByteStr for T {
        type Err = ParseFromStrError<T>;

        fn from_byte_str(s: &ByteStr) -> Result<T, Self::Err> {
          use self::ParseFromStrErrorKind::*;

          str::from_utf8(s.as_bytes())
            .map_err(|e| ParseFromStrError(Utf8Error(e)))
            .and_then(|s| s.parse().map_err(|e| ParseFromStrError(FromStrError(e))))
        }
      }
    }
  }

  pub mod io {
    pub use self::scanner::*;

    mod scanner {
      use spella::byte::{ByteStr, FromByteStr};

      use std::io::{self, BufRead};

      #[derive(Debug)]
      pub struct Scanner<R> {
        reader: R,
        buf: Vec<u8>,
        pos: usize,
      }

      const INITIAL_CAPACITY: usize = 32;

      impl<R: BufRead> Scanner<R> {
        pub fn new(reader: R) -> Self {
          Scanner {
            reader: reader,
            buf: Vec::with_capacity(INITIAL_CAPACITY),
            pos: 0,
          }
        }

        pub fn next<T: FromByteStr>(&mut self) -> io::Result<Result<T, T::Err>> {
          self.next_byte_str().map(T::from_byte_str)
        }

        pub fn next_byte_str(&mut self) -> io::Result<&ByteStr> {
          if self.buf.is_empty() {
            self.read_line()?;
          }

          loop {
            match self.buf.get(self.pos) {
              Some(&b' ') => self.pos += 1,
              Some(&b'\n') => self.read_line()?,
              Some(_) => break,
              None => return Err(io::Error::from(io::ErrorKind::UnexpectedEof)),
            }
          }

          let start = self.pos;
          self.pos += 1;

          loop {
            match self.buf.get(self.pos) {
              Some(&b' ') | Some(&b'\n') | None => break,
              Some(_) => self.pos += 1,
            }
          }

          Ok(ByteStr::from_bytes(&self.buf[start..self.pos]))
        }

        fn read_line(&mut self) -> io::Result<()> {
          self.buf.clear();
          self.pos = 0;
          self.reader.read_until(b'\n', &mut self.buf)?;

          Ok(())
        }
      }
    }
  }
}

mod prelude {
  pub use spella::byte::{ByteChar, ByteStr, ByteString};
  pub use std::collections::*;
  pub use std::io::prelude::*;
  pub use std::iter::FromIterator;
  pub use std::marker::PhantomData;
  pub use std::num::Wrapping;
  pub use std::ops::{Range, RangeFrom, RangeTo};
  pub use std::{cell, cmp, f64, i32, i64, isize, iter, mem, rc, str, time, u32, u64, usize};
}

use prelude::*;

const CUSTOM_STACK_SIZE_MEBIBYTES: Option<usize> = None;

fn main() {
  fn exec_solver() {
    let stdin = std::io::stdin();
    let stdout = std::io::stdout();
    #[cfg(not(debug_assertions))]
    let mut writer = std::io::BufWriter::new(stdout.lock());
    #[cfg(debug_assertions)]
    let mut writer = stdout.lock();
    solve(stdin.lock(), &mut writer);
    writer.flush().unwrap();
  }

  if let Some(stack_size_mebibytes) = CUSTOM_STACK_SIZE_MEBIBYTES {
    std::thread::Builder::new()
      .name("exec_solver".to_owned())
      .stack_size(stack_size_mebibytes * 1024 * 1024)
      .spawn(exec_solver)
      .unwrap()
      .join()
      .unwrap();
  } else {
    exec_solver();
  }
}

fn solve<R: BufRead, W: Write>(reader: R, mut writer: W) {
  let mut _scanner = spella::io::Scanner::new(reader);

  #[allow(unused_macros)]
  macro_rules! scan {
    ($T:ty) => {
      _scanner.next::<$T>().unwrap().unwrap()
    };
    ($($T:ty),+) => {
      ($(scan!($T)),+)
    };
    ($($T:ty),+; $n:expr $(; $m:expr)*) => {{
      (0..$n).map(|_| scan!($($T),+ $(; $m)*)).collect::<Vec<_>>()
    }};
  }

  #[allow(unused_macros)]
  macro_rules! scan_iter {
    ($($T:ty),+; $n:expr) => {
      (0..$n).map(|_| scan!($($T),+))
    };
  }

  #[allow(unused_macros)]
  macro_rules! print {
    ($fmt:expr) => {
      write!(writer, $fmt).unwrap()
    };
    ($fmt:expr, $($arg:tt)*) => {
      write!(writer, $fmt, $($arg)*).unwrap()
    };
  }

  #[allow(unused_macros)]
  macro_rules! println {
    ($fmt:expr) => {
      writeln!(writer, $fmt).unwrap()
    };
    ($fmt:expr, $($arg:tt)*) => {
      writeln!(writer, $fmt, $($arg)*).unwrap()
    };
  }

  #[allow(unused_macros)]
  macro_rules! eprint {
    ($fmt:expr) => {
      #[cfg(debug_assertions)]
      write!(std::io::stderr(), $fmt).unwrap()
    };
    ($fmt:expr, $($arg:tt)*) => {
      #[cfg(debug_assertions)]
      write!(std::io::stderr(), $fmt, $($arg)*).unwrap()
    };
  }

  #[allow(unused_macros)]
  macro_rules! eprintln {
    ($fmt:expr) => {
      #[cfg(debug_assertions)]
      writeln!(std::io::stderr(), $fmt).unwrap()
    };
    ($fmt:expr, $($arg:tt)*) => {
      #[cfg(debug_assertions)]
      writeln!(std::io::stderr(), $fmt, $($arg)*).unwrap()
    };
  }

  #[allow(unused_macros)]
  macro_rules! dbg {
    ($($x:expr),+) => {{
      eprintln!(concat!("[{}:{}] ", $(stringify!($x), " = {:?}; "),+), file!(), line!(), $($x),+);
    }};
  }

  let (n, m) = scan!(usize, usize);

  let mut max_l = 0;
  let mut min_r = n;

  for (l, r) in scan_iter!(usize, usize; m) {
    max_l = cmp::max(max_l, l);
    min_r = cmp::min(min_r, r);
  }

  let ans = if min_r >= max_l { min_r - max_l + 1 } else { 0 };
  println!("{}", ans);
}