// ---------- begin ModInt ---------- const MOD: u32 = 1_000_000_007; #[derive(Clone, Copy)] struct ModInt(u32); impl std::ops::Add for ModInt { type Output = ModInt; fn add(self, rhs: ModInt) -> Self::Output { let mut d = self.0 + rhs.0; if d >= MOD { d -= MOD; } ModInt(d) } } impl std::ops::AddAssign for ModInt { fn add_assign(&mut self, rhs: ModInt) { *self = *self + rhs; } } impl std::ops::Sub for ModInt { type Output = ModInt; fn sub(self, rhs: ModInt) -> Self::Output { let mut d = self.0 + MOD - rhs.0; if d >= MOD { d -= MOD; } ModInt(d) } } impl std::ops::SubAssign for ModInt { fn sub_assign(&mut self, rhs: ModInt) { *self = *self - rhs; } } impl std::ops::Mul for ModInt { type Output = ModInt; fn mul(self, rhs: ModInt) -> Self::Output { ModInt((self.0 as u64 * rhs.0 as u64 % MOD as u64) as u32) } } impl std::ops::MulAssign for ModInt { fn mul_assign(&mut self, rhs: ModInt) { *self = *self * rhs; } } impl std::ops::Neg for ModInt { type Output = ModInt; fn neg(self) -> Self::Output { ModInt(if self.0 == 0 {0} else {MOD - self.0}) } } /* impl std::fmt::Display for ModInt { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { write!(f, "{}", self.0) } } */ #[allow(dead_code)] impl ModInt { pub fn new(n: u32) -> ModInt { ModInt(n % MOD) } pub fn zero() -> ModInt { ModInt(0) } pub fn one() -> ModInt { ModInt(1) } pub fn pow(self, mut n: u32) -> ModInt { let mut t = ModInt::one(); let mut s = self; while n > 0 { if n & 1 == 1 { t *= s; } s *= s; n >>= 1; } t } pub fn inv(self) -> ModInt { self.pow(MOD - 2) } } // ---------- end ModInt ---------- // ---------- begin Precalc ---------- #[allow(dead_code)] struct Precalc { inv: Vec, fact: Vec, ifact: Vec, } #[allow(dead_code)] impl Precalc { pub fn new(n: usize) -> Precalc { let mut inv = vec![ModInt::one(); n + 1]; let mut fact = vec![ModInt::one(); n + 1]; let mut ifact = vec![ModInt::one(); n + 1]; for i in 2..(n + 1) { inv[i] = -inv[MOD as usize % i] * ModInt(MOD / i as u32); fact[i] = fact[i - 1] * ModInt(i as u32); ifact[i] = ifact[i - 1] * inv[i]; } Precalc { inv: inv, fact: fact, ifact: ifact, } } pub fn inv(&self, n: usize) -> ModInt { self.inv[n] } pub fn fact(&self, n: usize) -> ModInt { self.fact[n] } pub fn ifact(&self, n: usize) -> ModInt { self.ifact[n] } pub fn comb(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[k] * self.ifact[n - k] } } // ---------- end Precalc ---------- use std::cmp::{max, min}; fn run() { let mut s = String::new(); std::io::stdin().read_line(&mut s).unwrap(); let mut it = s.trim().split_whitespace(); let d: usize = it.next().unwrap().parse().unwrap(); let l: usize = it.next().unwrap().parse().unwrap(); let r: usize = it.next().unwrap().parse().unwrap(); let k: usize = it.next().unwrap().parse().unwrap(); let x = (l + 1).next_power_of_two().trailing_zeros() as usize; let y = (r + 1).next_power_of_two().trailing_zeros() as usize; let (x, y) = (max(x, y), min(x, y)); if k < x - y || x - 1 + y - 1 < k || (k - (x - y)) % 2 != 0 { println!("0"); return; } let p = y - (k - (x - y)) / 2; assert!(x - p + y - p == k); let mut ans = ModInt::new((1 << (p - 1)) as u32); ans *= ModInt(2).pow((x - p) as u32); if p != y { ans *= ModInt(2).pow((y - p - 1) as u32); } for i in 1..=d { for j in 1..=(1 << (i - 1)) { ans *= ModInt(j as u32); } } ans *= ModInt((1 << (x - 1)) as u32).inv(); if x == y { ans *= ModInt((1 << (y - 1)) as u32 - 1).inv(); } else { ans *= ModInt((1 << (y - 1)) as u32).inv(); } println!("{}", ans.0); } fn main() { run(); }