Problem:
Score : 1000 points

Problem Statement

Snuke arranged N colorful balls in a row.
The i-th ball from the left has color c_i and weight w_i.

He can rearrange the balls by performing the following two operations any number of times, in any order:

Operation 1: Select two balls with the same color. If the total weight of these balls is at most X, swap the positions of these balls.

Operation 2: Select two balls with different colors. If the total weight of these balls is at most Y, swap the positions of these balls.

How many different sequences of colors of balls can be obtained? Find the count modulo 10^9 + 7.

Constraints

1 ≤ N ≤ 2 × 10^5

1 ≤ X, Y ≤ 10^9

1 ≤ c_i ≤ N

1 ≤ w_i ≤ 10^9

X, Y, c_i, w_i are all integers.

Input

Input is given from Standard Input in the following format:

N X Y
c_1 w_1
:
c_N w_N

Output

Print the answer.

Sample Input 1

4 7 3
3 2
4 3
2 1
4 4

Sample Output 1

2

The sequence of colors (2,4,3,4) can be obtained by swapping the positions of the first and third balls by operation 2.

It is also possible to swap the positions of the second and fourth balls by operation 1, but it does not affect the sequence of colors.

Sample Input 2

1 1 1
1 1

Sample Output 2

1

Sample Input 3

21 77 68
16 73
16 99
19 66
2 87
2 16
7 17
10 36
10 68
2 38
10 74
13 55
21 21
3 7
12 41
13 88
18 6
2 12
13 87
1 9
2 27
13 15

Sample Output 3

129729600

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

// use std::ops::{Index, IndexMut};
// use std::cmp::{Ordering, min, max};
// use std::collections::{BinaryHeap, BTreeMap};
// use std::collections::btree_map::Entry::{Occupied, Vacant};
// use std::clone::Clone;

fn getline() -> String{
    let mut res = String::new();
    std::io::stdin().read_line(&mut res).ok();
    res
}

macro_rules! readl {
    ($t: ty) => {
        {
            let s = getline();
            s.trim().parse::<$t>().unwrap()
        }
    };
    ($( $t: ty),+ ) => {
        {
            let s = getline();
            let mut iter = s.trim().split(' ');
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*) 
        }
    };
}

macro_rules! readlvec {
    ($t: ty) => {
        {
            let s = getline();
            let iter = s.trim().split(' ');
            iter.map(|x| x.parse().unwrap()).collect::<Vec<$t>>()
        }
    }
}

macro_rules! mvec {
    ($v: expr, $s: expr) => {
        vec![$v; $s]
    };
    ($v: expr, $s: expr, $($t: expr),*) => {
        vec![mvec!($v, $($t),*); $s]
    };
}

macro_rules! debug {
    ($x: expr) => {
        println!("{}: {:?}", stringify!($x), $x)
    }
}

fn printiter<'a, T>(v: &'a T)
where
    &'a T: std::iter::IntoIterator, 
    <&'a T as std::iter::IntoIterator>::Item: std::fmt::Display {
    for (i,e) in v.into_iter().enumerate() {
        if i != 0 {
            print!(" ");
        }
        print!("{}", e);
    }
    println!("");
}

trait BinarySearch {
    type E;
    fn lower_bound(&self, &(Self::E)) -> usize;
    fn upper_bound(&self, &(Self::E)) -> usize;
}

impl<T> BinarySearch for Vec<T>
where T: std::cmp::Ord {
    type E = T;
    fn lower_bound(&self, e: &(Self::E)) -> usize {
         match self.binary_search(e) {
             Ok(p) => p,
             Err(p) => p,
         }
    }
    fn upper_bound(&self, e: &(Self::E)) -> usize {
        match self.binary_search(e) {
            Ok(p) => p+1,
            Err(p) => p,
        }
    }
}

macro_rules! make_modint {
    ($MOD: expr, $name: ident) => {
        struct $name {
            val: i64,
        }

        impl $name {
            fn new(x: i64) -> $name {
                let x = x%$MOD;
                $name{val: if x < 0 { x+$MOD } else { x }}
            }

            fn pow(&self, x: i64) -> $name {
                let mut res = $name::new(1);
                let mut tmp = x;
                let mut p = *self;
                while tmp != 0 {
                    if tmp&1 == 1 {
                        res *= p;
                    }
                    tmp = tmp>>1;
                    p = p*p;
                }
                res
            }

            fn inv(&self) -> $name {
                assert!(self.val != 0);
                let mut a = self.val;
                let mut b = $MOD;
                let mut u = 1;
                let mut v = 0;
                use std::mem::swap;
                while b != 0 {
                    let t = a/b;
                    a -= t*b;
                    swap(&mut a, &mut b);
                    u -= t*v;
                    swap(&mut u, &mut v);
                }
                $name::new(u)
            }
        }

        impl std::clone::Clone for $name {
            fn clone(&self) -> $name {
                $name{ val: self.val }
            }
        }

        impl std::marker::Copy for $name { }

        impl std::ops::Add for $name {
            type Output = $name;
            fn add(self, y: $name) -> $name {
                let tmp = self.val+y.val;
                $name{val: if tmp >= $MOD {tmp-$MOD} else {tmp}}
            }
        }

        impl std::ops::Neg for $name {
            type Output = $name;
            fn neg(self) -> $name {
                $name::new(self.val)
            }
        }

        impl std::ops::Sub for $name {
            type Output = $name;
            fn sub(self, other: $name) -> $name{
                let tmp = self.val-other.val;
                $name{val: if tmp < 0 {tmp+$MOD} else {tmp}}
            }
        }

        impl std::ops::Mul for $name {
            type Output = $name;
            fn mul(self, y: $name) -> $name {
                $name{val: (self.val*y.val)%$MOD}
            }
        }

        impl std::ops::Div for $name {
            type Output = $name;
            fn div(self, other: $name) -> $name {
                self*other.inv()
            }
        }

        impl std::fmt::Display for $name {
            fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
                write!(f, "{}", self.val)
            }
        }

        impl std::ops::AddAssign for $name {
        fn add_assign(&mut self, other: $name) {
            *self = *self+other;
        }
        }

        impl std::ops::SubAssign for $name {
            fn sub_assign(&mut self, other: $name) {
                *self = *self-other;
            }
        }

        impl std::ops::MulAssign for $name {
            fn mul_assign(&mut self, other: $name) {
                *self = *self*other;
            }
        }

        impl std::ops::DivAssign for $name {
            fn div_assign(&mut self, other: $name) {
                *self = *self*other.inv();
            }
        }

        impl std::fmt::Debug for $name {
            fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
                write!(f, "{}", self.val)
            }
        }
    }
}

make_modint!(1_000_000_000+7, ModInt);

fn mint(x: i64) -> ModInt {
    ModInt::new(x)
}

#[derive(Debug)]
struct ConvQuery<T> 
    where T: algebra::Field  {
    fac: Vec<T>,
    facinv: Vec<T>,
}

mod algebra {
    use std::ops::{Add, Mul, Neg, Sub, Div};
    use std;

    pub trait Zero {
        fn Zero() -> Self;
    }
    
    pub trait Monoid: Add<Self, Output=Self>+Zero 
        where Self : std::marker::Sized{
    }

    pub trait Group: Monoid+Neg+Sub<Self, Output=Self> {
    }

    pub trait Ring: Group+Mul<Self, Output=Self> {
    }

    pub trait One {
        fn One() -> Self;
    }

    pub trait Field: Ring+One+Div<Self, Output=Self> {
    }
}

impl algebra::One for ModInt {
    fn One() -> Self {
        ModInt{val: 1}
    }
}

impl algebra::Zero for ModInt {
    fn Zero() -> Self {
        ModInt{val: 0}
    }
}

impl algebra::Monoid for ModInt {}

impl algebra::Group for ModInt {}

impl algebra::Ring for ModInt {}

impl algebra::Field for ModInt {}

trait MapToi64 {
    fn map_to_number(i64) -> Self;
}

impl MapToi64 for ModInt {
    fn map_to_number(x: i64) -> ModInt {
        ModInt::new(x)
    }
}

impl<T> ConvQuery<T>
    where T: algebra::Field+MapToi64+std::clone::Clone {
    
    fn new(n: usize) -> Self {
        let mut fac = Vec::with_capacity(n+1);
        let mut facinv = Vec::with_capacity(n+1);
        fac.push(T::One());
        for x in 1..n+1 {
            let num = {
                let last = fac.last().unwrap();
                (*last).clone() * T::map_to_number(x as i64)
            };
            fac.push(num.clone());
        }
        let mut num = T::One()/fac.last().unwrap().clone();
        facinv.push(num.clone());
        for i in (0..n).rev() {
            num = num * T::map_to_number((i+1) as i64);
            facinv.push(num.clone());
        }
        facinv.reverse();
        ConvQuery {
            fac: fac,
            facinv: facinv,
        }
    }

    fn query(&self, n: usize, m: usize) -> T {
        self.fac[n].clone() * self.facinv[n-m].clone() * self.facinv[m].clone()
    }
}


fn main() {
    let (n, x, y) = readl!(usize, i64, i64);
    let mut c = Vec::with_capacity(n);
    let mut w = Vec::with_capacity(n);
    for _ in 0..n {
        let (a, b) = readl!(usize, i64);
        c.push(a);
        w.push(b);
    }
    let c = c;
    let w = w;

    let mut cw = std::collections::HashMap::new();
    for i in 0..n {
        let vec = cw.entry(c[i]).or_insert(Vec::new());
        vec.push(w[i]);
    }

    let mut com = Vec::new();    
    for (&c, vec) in &mut cw {
        vec.sort();
        let bo = vec.upper_bound(&(x-(*vec)[0]));
        if bo != 0 {
            com.push((vec[0], bo, c));
        }
        for i in bo..vec.len() {
            com.push((vec[i], 1, c));
        }
    }
    com.sort();
    let com = com;

    let (mi, num, color) = com[0];
    let mut ans = mint(1);
    let mut map = std::collections::HashMap::new();
    for &(val, num, color) in &com {
        if val+mi <= y {
            let t = map.entry(color).or_insert(0);
            *t += num;
        }
    }
    let C = ConvQuery::<ModInt>::new(n+2);
    let mut sum = 0;
    for (_, &val) in &map {
        sum += val;
        ans *= C.query(sum, val);
    }
    println!("{}", ans);
}