macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; // var... 変数の識別子, $t...型を一つよむ ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); //ここで繰り返し input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; // ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; // 配列の最後のNestではここで型が指定されてparseされる ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; // var... 変数の識別子, $t...型を一つよむ ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); //ここで繰り返し input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; // ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; // 配列の最後のNestではここで型が指定されてparseされる ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ========= pub trait ModI: Sized + PartialEq + Copy + std::ops::Add + std::ops::Sub + std::ops::Mul + std::ops::Div + std::ops::AddAssign + std::ops::SubAssign + std::ops::MulAssign + std::ops::DivAssign + std::default::Default + std::fmt::Display + std::fmt::Debug { fn m() -> u64; fn new(x: u64) -> Self; fn pow(self, n: u64) -> Self; fn inv(&self) -> Self; } macro_rules! define_modint { ($n:ident,$m:expr) => { #[derive(Clone, Copy, Eq, PartialEq, PartialOrd, Ord)] struct $n(u64); #[allow(dead_code)] impl ModI for $n { fn m() -> u64 { $m } fn new(x: u64) -> $n { $n(x % $m) } fn pow(self, mut n: u64) -> $n { let mut ret = $n::new(1); let mut base = self; while n > 0 { if n & 1 == 1 { ret *= base; } base *= base; n >>= 1; } ret } fn inv(&self) -> $n { self.pow($m - 2) } } impl std::default::Default for $n { fn default() -> $n { $n::new(0u64) } } impl std::convert::From for $n { fn from(x: u64) -> $n { $n::new(x) } } // Binary operator impl std::ops::Add for $n { type Output = $n; fn add(self, rhs: $n) -> Self::Output { $n::new(self.0 + rhs.0) } } impl std::ops::Sub for $n { type Output = $n; fn sub(self, rhs: $n) -> Self::Output { if self.0 >= rhs.0 { $n::new(self.0 - rhs.0) } else { $n::new($m - rhs.0 + self.0) } } } impl std::ops::Mul for $n { type Output = $n; fn mul(self, rhs: $n) -> Self::Output { $n::new(self.0 * rhs.0) } } impl std::ops::Div for $n { type Output = $n; fn div(self, rhs: $n) -> Self::Output { $n::new(self.0 / rhs.0) } } // Assign impl std::ops::AddAssign for $n { fn add_assign(&mut self, rhs: $n) { *self = *self + rhs; } } impl std::ops::SubAssign for $n { fn sub_assign(&mut self, rhs: $n) { *self = *self - rhs; } } impl std::ops::MulAssign for $n { fn mul_assign(&mut self, rhs: $n) { *self = *self * rhs; } } impl std::ops::DivAssign for $n { fn div_assign(&mut self, rhs: $n) { *self = *self / rhs; } } impl std::fmt::Display for $n { fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::fmt::Debug for $n { fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result { write!(f, "{}", self.0) } } }; } // 10^8 < p < 10^9 // 3 is primitive p-1 root of these // 167772161 = 5*2^25 + 1, 469762049 = 7*2^26 + 1, 998244353 = 119*2^23 + 1 // 1224736769 = 73 * 2^24 + 1 // define_modint!(ModInt167772161, 167772161); define_modint!(ModInt998244353, 998244353); define_modint!(ModInt1224736769, 1224736769); fn ntt(a: &mut [T], n: usize, inv: bool) { // h = log2(n) let h = { let mut i = 0; while 1 << i != n { i += 1; } i }; let mut j: usize; for i in 0..n { j = 0; for k in 0..h { // (i >> k & 1)はiのk桁目のbit // (h - 1 - k)は全体をh-bitとしてk桁目の反対の位置 j |= (i >> k & 1) << (h - 1 - k); } // はじめの一回だけひっくりかえす if i < j { a.swap(i, j) }; } // バタフライ演算 let mut b = 1; while b < n { let zeta: T = T::new(3).pow((T::m() - 1) / (2 * b as u64)); for j in 0..b { // 3 is primitive root of proth prime // 3 ^ ((m - 1) / (n * j)) is primitive n root's j power let e: T = if inv { zeta.pow(j as u64).inv() } else { zeta.pow(j as u64) }; let mut k = 0; while k < n { let s: T = a[j + k]; let t: T = a[j + k + b] * e; a[j + k] = s + t; a[j + k + b] = s - t; k += b * 2; } } b *= 2; } if inv { let ni = T::new(n as u64).inv(); for i in 0..n { a[i] *= ni; } } } fn mod_conv(mut a: &mut [T], mut b: &mut [T]) -> Vec { let n = a.len(); // calc each mod ntt(&mut a, n, false); ntt(&mut b, n, false); let mut c = Vec::with_capacity(n); for i in 0..n { c.push(a[i] * b[i]); } ntt(&mut c, n, true); c } fn single_convolution(a: &mut [T], b: &mut [T]) -> Vec { let d: usize = a.len() + b.len() - 1; let n = d.checked_next_power_of_two().unwrap(); let mut a = a.to_vec(); a.resize(n, T::new(0)); let mut b = b.to_vec(); b.resize(n, T::new(0)); let mut res = mod_conv(&mut a, &mut b); res.truncate(d); res } fn mod_pow(mut a: u64, mut n: u64, m: u64) -> u64 { let mut ret = 1; while n > 0 { if n & 1 == 1 { ret *= a; ret %= m; } a *= a; a %= m; n >>= 1; } ret } // mod mの体におけるaの逆元 fn mod_inv(a: u64, m: u64) -> u64 { mod_pow(a, m - 2, m) } fn garner(mr: &mut Vec<(u64, u64)>, m: u64) -> u64 { mr.push((m, 0)); // coef... mixed radixの係数, constants... 前まで求めた係数 let mut coef: Vec = vec![1; mr.len()]; let mut constants: Vec = vec![0; mr.len()]; for i in 0..mr.len() - 1 { let v: u64 = (mr[i].1 + mr[i].0 - constants[i]) * mod_inv(coef[i], mr[i].0) % mr[i].0; for j in i + 1..mr.len() { constants[j] += coef[j] * v; constants[j] %= mr[j].0; coef[j] *= mr[i].0; coef[j] %= mr[j].0; } } constants[mr.len() - 1] } // for more bigger number fn convolution(a: &[u64], b: &[u64]) -> Vec { let d: usize = a.len() + b.len() - 1; let n = d.checked_next_power_of_two().unwrap(); let mut a = a.to_vec(); a.resize(n, 0); let mut b = b.to_vec(); b.resize(n, 0); type F0 = ModInt1224736769; type F1 = ModInt998244353; let mut a0: Vec = a.iter().map(|e| F0::new(*e)).collect(); let mut b0: Vec = b.iter().map(|e| F0::new(*e)).collect(); let res0 = single_convolution(&mut a0, &mut b0); let mut a1: Vec = a.iter().map(|e| F1::new(*e)).collect(); let mut b1: Vec = b.iter().map(|e| F1::new(*e)).collect(); let res1 = single_convolution(&mut a1, &mut b1); let mut res: Vec = vec![]; for i in 0..res0.len() { let mut mr = vec![(1224736769u64, res0[i].0), (998244353u64, res1[i].0)]; let v = garner(&mut mr, std::u64::MAX); res.push(v); } res } fn main() { input! { n:usize, x:usize, a: [usize;n] } let mut a = a; a.sort(); let size = a[n - 1] + 1; let mut a0 = vec![0; size]; let mut b0 = vec![0; size]; for e in a { a0[e] += 1; b0[e] += 1; } let res = convolution(&a0, &b0); if x < size * 2 - 1 { println!("{:?}", res[x]); } else { println!("{:?}", 0); } }