結果

問題 No.890 移調の限られた旋法
ユーザー akakimidoriakakimidori
提出日時 2019-09-20 22:01:33
言語 Rust
(1.77.0)
結果
AC  
実行時間 23 ms / 2,000 ms
コード長 4,482 bytes
コンパイル時間 3,265 ms
コンパイル使用メモリ 148,356 KB
実行使用メモリ 13,584 KB
最終ジャッジ日時 2023-10-12 19:08:29
合計ジャッジ時間 5,209 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge14
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 1 ms
4,348 KB
testcase_01 AC 1 ms
4,352 KB
testcase_02 AC 1 ms
4,352 KB
testcase_03 AC 1 ms
4,352 KB
testcase_04 AC 1 ms
4,348 KB
testcase_05 AC 1 ms
4,348 KB
testcase_06 AC 1 ms
4,352 KB
testcase_07 AC 1 ms
4,352 KB
testcase_08 AC 1 ms
4,348 KB
testcase_09 AC 1 ms
4,348 KB
testcase_10 AC 1 ms
4,348 KB
testcase_11 AC 1 ms
4,348 KB
testcase_12 AC 1 ms
4,348 KB
testcase_13 AC 23 ms
13,564 KB
testcase_14 AC 1 ms
4,352 KB
testcase_15 AC 22 ms
13,584 KB
testcase_16 AC 22 ms
13,564 KB
testcase_17 AC 21 ms
12,320 KB
testcase_18 AC 21 ms
12,316 KB
testcase_19 AC 12 ms
8,028 KB
testcase_20 AC 1 ms
4,352 KB
testcase_21 AC 1 ms
4,352 KB
testcase_22 AC 18 ms
10,792 KB
testcase_23 AC 1 ms
4,348 KB
testcase_24 AC 14 ms
8,204 KB
testcase_25 AC 1 ms
4,348 KB
testcase_26 AC 22 ms
13,008 KB
testcase_27 AC 22 ms
13,332 KB
testcase_28 AC 1 ms
4,352 KB
testcase_29 AC 10 ms
6,644 KB
testcase_30 AC 21 ms
12,312 KB
testcase_31 AC 12 ms
7,716 KB
testcase_32 AC 19 ms
11,524 KB
testcase_33 AC 20 ms
12,344 KB
testcase_34 AC 21 ms
12,288 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

// ---------- 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)
    }
    pub fn comb(n: u32, k: u32) -> ModInt {
        if k > n {
            return ModInt::zero();
        }
        let k = std::cmp::min(k, n - k);
        let mut nu = ModInt::one();
        let mut de = ModInt::one();
        for i in 0..k {
            nu *= ModInt(n - i);
            de *= ModInt(i + 1);
        }
        nu * de.inv()
    }
}

#[allow(dead_code)]
struct Precalc {
    inv: Vec<ModInt>,
    fact: Vec<ModInt>,
    ifact: Vec<ModInt>,
}

#[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 ModInt ----------
fn gcd(a: usize, b: usize) -> usize {
    if b == 0 {a} else {gcd(b, a % b)}
}

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 k: usize = it.next().unwrap().parse().unwrap();
    let mut g = gcd(n, k);
    if g == 1 {
        println!("0");
        return;
    }
    let mut d = 2;
    let mut p = vec![];
    while d * d <= g {
        if g % d == 0 {
            p.push(d);
            while g % d == 0 {
                g /= d;
            }
        }
        d += 1;
    }
    if g > 1 {
        p.push(g);
    }
    let pc = Precalc::new(n);
    let mut ans = ModInt::zero();
    let len = p.len();
    for i in 1..(1 << len) {
        let mut f = 1;
        let mut sign = -ModInt::one();
        for j in 0..len {
            if (i >> j) & 1 == 1 {
                f *= p[j];
                sign = -sign;
            }
        }
        ans += sign * pc.comb(n / f, k / f);
    }
    println!("{}", ans);
}

fn main() {
    run();
}
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