// ---------- 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<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::str::FromStr for ModInt { type Err = std::num::ParseIntError; fn from_str(s: &str) -> Result { let val = s.parse::()?; Ok(ModInt::new(val)) } } #[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 { assert!(self.0 > 0); self.pow(MOD - 2) } } // ---------- end ModInt ---------- // ---------- begin karatsuba multiplication ---------- fn karatsuba(a: &[T], b: &[T], c: &mut [T], zero: T, buf: &mut [T]) where T: std::marker::Copy + std::ops::Add + std::ops::Sub + std::ops::Mul + { assert!(a.len() == b.len()); let n = a.len(); if n <= 16 { for (i, a) in a.iter().enumerate() { for (c, b) in c[i..].iter_mut().zip(b.iter()) { *c = *c + *a * *b; } } return; } if n & 1 == 1 { karatsuba(&a[1..], &b[1..], &mut c[2..], zero, buf); let x = a[0]; let y = b[0]; c[0] = c[0] + x * y; for (c, (a, b)) in c[1..].iter_mut().zip(a[1..].iter().zip(b[1..].iter())) { *c = *c + x * *b + *a * y; } return; } let m = n / 2; karatsuba(&a[..m], &b[..m], &mut c[..n], zero, buf); karatsuba(&a[m..], &b[m..], &mut c[n..], zero, buf); let (x, buf) = buf.split_at_mut(m); let (y, buf) = buf.split_at_mut(m); let (z, buf) = buf.split_at_mut(n); for z in z.iter_mut() { *z = zero; } for (x, (p, q)) in x.iter_mut().zip(a.iter().zip(a[m..].iter())) { *x = *p + *q; } for (y, (p, q)) in y.iter_mut().zip(b.iter().zip(b[m..].iter())) { *y = *p + *q; } karatsuba(x, y, z, zero, buf); for (z, (p, q)) in z.iter_mut().zip(c[..n].iter().zip(c[n..].iter())) { *z = *z - (*p + *q); } for (c, z) in c[m..].iter_mut().zip(z.iter()) { *c = *c + *z; } } fn multiply(a: &[T], b: &[T], zero: T) -> Vec where T: std::marker::Copy + std::ops::Add + std::ops::Sub + std::ops::Mul + { let mut i = 0; let mut j = 0; let mut ans = vec![zero; a.len() + b.len()]; let mut buf = vec![zero; 4 * (a.len() + b.len())]; let mut c = Vec::with_capacity(a.len() + b.len()); while i < a.len() && j < b.len() { let x = a.len() - i; let y = b.len() - j; let z = std::cmp::min(x, y); c.clear(); c.resize(2 * z, zero); karatsuba(&a[i..(i + z)], &b[j..(j + z)], &mut c, zero, &mut buf); for (ans, c) in ans[(i + j)..].iter_mut().zip(c.iter()) { *ans = *ans + *c; } if x <= y { j += x; } else { i += y; } } ans.truncate(a.len() + b.len() - 1); ans } // ---------- end karatsuba multiplication ---------- fn run() { let mut s = String::new(); std::io::stdin().read_line(&mut s).unwrap(); let mut it = s.trim().split_whitespace(); let n: usize = it.next().unwrap().parse().unwrap(); let d: usize = it.next().unwrap().parse().unwrap(); let k: usize = it.next().unwrap().parse().unwrap(); let mut t = vec![ModInt::one()]; let mut s = vec![ModInt::one(); d + 1]; s[0] = ModInt::zero(); for i in 0..9 { if (n >> i) & 1 == 1 { t = multiply(&t, &s, ModInt::zero()); t.truncate(k + 1); } s = multiply(&s, &s, ModInt::zero()); s.truncate(k + 1); } println!("{}", t.get(k).map_or(ModInt::zero(), |t| *t)); } fn main() { run(); }