#373286 (Rust) No.802 だいたい等差数列

• 問題: No.802 だいたい等差数列
• ユーザー: akakimidori
• 提出日時: 2019-08-29 10:43:46
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 24 ms / 2,000 ms
• コード長: 4,992 bytes
• コンパイル時間: 9,737 ms
• コンパイル使用メモリ: 402,976 KB
• 実行使用メモリ: 17,172 KB
• 最終ジャッジ日時: 2024-11-17 16:49:36
• 合計ジャッジ時間: 11,124 ms
• ジャッジサーバーID （参考情報）: judge5 / judge3

ファイルパターン	結果
sample	AC * 4
other	AC * 30

ソースコード

// ---------- begin ModInt ----------
//https://github.com/kenkoooo/competitive-programming-rs/blob/master/src/math/mod_int.rs
//を参考にしています
#[allow(dead_code)]
mod modint {
    pub const MOD: u32 = 1_000_000_007;
    use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
    #[derive(Clone, Copy)]
    pub struct ModInt<T: Copy + Clone>(pub T);
    type Num = u32;
    impl Add<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn add(self, other: ModInt<Num>) -> ModInt<Num> {
            let mut d = self.0 + other.0;
            if d >= MOD {
                d -= MOD;
            }
            ModInt(d)
        }
    }
    impl AddAssign<ModInt<Num>> for ModInt<Num> {
        fn add_assign(&mut self, other: ModInt<Num>) {
            *self = *self + other;
        }
    }
    impl Sub<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn sub(self, other: ModInt<Num>) -> ModInt<Num> {
            let mut d = self.0 + MOD - other.0;
            if d >= MOD {
                d -= MOD;
            }
            ModInt(d)
        }
    }
    impl SubAssign<ModInt<Num>> for ModInt<Num> {
        fn sub_assign(&mut self, other: ModInt<Num>) {
            *self = *self - other;
        }
    }
    impl Mul<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn mul(self, other: ModInt<Num>) -> ModInt<Num> {
            ModInt(((self.0 as u64) * (other.0 as u64) % (MOD as u64)) as u32)
        }
    }
    impl MulAssign<ModInt<Num>> for ModInt<Num> {
        fn mul_assign(&mut self, other: ModInt<Num>) {
            *self = *self * other;
        }
    }
    impl Div<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn div(self, other: ModInt<Num>) -> ModInt<Num> {
            self * other.pow(MOD - 2)
        }
    }
    impl DivAssign<ModInt<Num>> for ModInt<Num> {
        fn div_assign(&mut self, other: ModInt<Num>) {
            *self = *self / other;
        }
    }
    impl Neg for ModInt<Num> {
        type Output = ModInt<Num>;
        fn neg(self) -> ModInt<Num> {
            ModInt(if self.0 == 0 { 0 } else { MOD - self.0 })
        }
    }
    impl ModInt<Num> {
        pub fn new(v: u32) -> ModInt<Num> {
            ModInt(v % MOD)
        }
        pub fn pow(self, mut n: u32) -> ModInt<Num> {
            let mut t = ModInt::new(1);
            let mut s = self;
            while n > 0 {
                if (n & 1) == 1 {
                    t *= s;
                }
                s *= s;
                n >>= 1;
            }
            t
        }
    }
    pub struct Precalc {
        n: usize,
        inv: Vec<ModInt<Num>>,
        fact: Vec<ModInt<Num>>,
        ifact: Vec<ModInt<Num>>,
    }
    impl Precalc {
        pub fn new(n: usize) -> Precalc {
            let mut inv = vec![ModInt(1); n + 1];
            let mut fact = vec![ModInt(1); n + 1];
            let mut ifact = vec![ModInt(1); n + 1];
            for i in 1..(n + 1) {
                if i >= 2 {
                    inv[i] = -inv[(MOD as usize) % i] * ModInt(MOD / (i as u32));
                }
                fact[i] = ModInt(i as u32) * fact[i - 1];
                ifact[i] = inv[i] * ifact[i - 1];
            }
            Precalc {
                n: n,
                inv: inv,
                fact: fact,
                ifact: ifact,
            }
        }
        pub fn fact(&self, n: usize) -> ModInt<Num> {
            self.fact[n]
        }
        pub fn inv(&self, x: usize) -> ModInt<Num> {
            self.inv[x]
        }
        pub fn ifact(&self, x: usize) -> ModInt<Num> {
            self.ifact[x]
        }
        pub fn comb(&self, n: usize, k: usize) -> ModInt<Num> {
            if !(k <= n) {
                return ModInt(0);
            }
            self.fact[n] * self.ifact[k] * self.ifact[n - k]
        }
    }
    use std;
    impl std::fmt::Display for ModInt<Num> {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }
}
// ---------- end ModInt ----------

use modint::*;

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 m: usize = it.next().unwrap().parse().unwrap();
    let d1: usize = it.next().unwrap().parse().unwrap();
    let d2: usize = it.next().unwrap().parse().unwrap();
    if 1 + d1 * (n - 1) > m {
        println!("0");
        return;
    }
    let d = d2 - d1;
    let m = m - 1 - d1 * (n - 1);
    let pc = Precalc::new(n + m + 1);
    let mut ans = pc.comb(m + n, n);
    let mut sign = -ModInt(1);
    let mut i = 1;
    while i <= n - 1 && i * (d + 1) <= m {
        ans += sign * pc.comb(n - 1, i) * pc.comb(m + n - i * (d + 1), n);
        sign = -sign;
        i += 1;
    }
    println!("{}", ans);
}

fn main() {
    run();
}