General

# Author Problem Lang Verdict Time Memory Sent Judged
122501863 Contestant:
sansen
1550C - 6 Rust Wrong answer on test 1 0 ms 6060 KB 2021-07-14 19:13:51 2021-07-14 19:13:51

→ Source
// ---------- begin ModInt ----------
// モンゴメリ乗算を用いる
// ほぼCodeforces用
// 注意
// new_unchecked は値xが 0 <= x < modulo であることを仮定
// ModInt の中身は正規化された値で持ってるので直接読んだり書いたりするとぶっ壊れる
// 奇素数のみ
mod modint {

use std::marker::*;
use std::ops::*;

pub trait Modulo {
fn modulo() -> u32;
fn rem() -> u32;
fn ini() -> u64;
fn reduce(x: u64) -> u32 {
assert!(x < (Self::modulo() as u64) << 32);
let b = (x as u32 * Self::rem()) as u64;
let t = x + b * Self::modulo() as u64;
let mut c = (t >> 32) as u32;
if c >= Self::modulo() {
c -= Self::modulo();
}
c as u32
}
}

pub enum Mod1_000_000_007 {}

impl Modulo for Mod1_000_000_007 {
fn modulo() -> u32 {
1_000_000_007
}
fn rem() -> u32 {
2226617417
}
fn ini() -> u64 {
582344008
}
}

pub enum Mod998_244_353 {}

impl Modulo for Mod998_244_353 {
fn modulo() -> u32 {
998_244_353
}
fn rem() -> u32 {
998244351
}
fn ini() -> u64 {
932051910
}
}

pub fn generate_umekomi_modulo(p: u32) {
assert!(p < (1 << 31) && p > 2 && p & 1 == 1 && (2u32..).take_while(|v| v * v <= p).all(|k| p % k != 0));
let mut t = 1u32;
let mut s = !p + 1;
let mut n = !0u32 >> 2;
while n > 0 {
if n & 1 == 1 {
t *= s;
}
s *= s;
n >>= 1;
}
let mut ini = (1u64 << 32) % p as u64;
ini = (ini << 32) % p as u64;
assert!(t * p == !0);
println!("pub enum Mod{} {{}}", p);
println!("impl Modulo for Mod{} {{", p);
println!("    fn modulo() -> u32 {{");
println!("        {}", p);
println!("    }}");
println!("    fn rem() -> u32 {{");
println!("        {}", t);
println!("    }}");
println!("    fn ini() -> u32 {{");
println!("        {}", ini);
println!("    }}");
println!("}}");
let mut f = vec![];
let mut n = p - 1;
for i in 2.. {
if i * i > n {
break;
}
if n % i == 0 {
f.push(i);
while n % i == 0 {
n /= i;
}
}
}
if n > 1 {
f.push(n);
}
let mut order = 1;
let mut n = p - 1;
while n % 2 == 0 {
n /= 2;
order <<= 1;
}
let z = (2u64..).find(|z| {
f.iter().all(|f| mod_pow(*z, ((p - 1) / *f) as u64, p as u64) != 1)
}).unwrap();
let zeta = mod_pow(z, ((p - 1) / order) as u64, p as u64);
println!("impl transform::NTTFriendly for Mod{} {{", p);
println!("    fn order() -> usize {{");
println!("        {}", order);
println!("    }}");
println!("    fn zeta() -> u32 {{");
println!("        {}", zeta);
println!("    }}");
println!("}}");
}

pub struct ModInt<T>(u32, PhantomData<T>);

impl<T> Clone for ModInt<T> {
fn clone(&self) -> Self {
ModInt::build(self.0)
}
}

impl<T> Copy for ModInt<T> {}

impl<T: Modulo> Add for ModInt<T> {
type Output = ModInt<T>;
fn add(self, rhs: Self) -> Self::Output {
let mut d = self.0 + rhs.0;
if d >= T::modulo() {
d -= T::modulo();
}
Self::build(d)
}
}

impl<T: Modulo> AddAssign for ModInt<T> {
fn add_assign(&mut self, rhs: Self) {
*self = *self + rhs;
}
}

impl<T: Modulo> Sub for ModInt<T> {
type Output = ModInt<T>;
fn sub(self, rhs: Self) -> Self::Output {
let mut d = self.0 - rhs.0;
if d >= T::modulo() {
d += T::modulo();
}
Self::build(d)
}
}

impl<T: Modulo> SubAssign for ModInt<T> {
fn sub_assign(&mut self, rhs: Self) {
*self = *self - rhs;
}
}

impl<T: Modulo> Mul for ModInt<T> {
type Output = ModInt<T>;
fn mul(self, rhs: Self) -> Self::Output {
Self::build(T::reduce(self.0 as u64 * rhs.0 as u64))
}
}

impl<T: Modulo> MulAssign for ModInt<T> {
fn mul_assign(&mut self, rhs: Self) {
*self = *self * rhs;
}
}

impl<T: Modulo> Neg for ModInt<T> {
type Output = ModInt<T>;
fn neg(self) -> Self::Output {
if self.0 == 0 {
Self::zero()
} else {
Self::build(T::modulo() - self.0)
}
}
}

impl<T: Modulo> std::fmt::Display for ModInt<T> {
fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
write!(f, "{}", self.get())
}
}

impl<T: Modulo> std::fmt::Debug for ModInt<T> {
fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
write!(f, "{}", self.get())
}
}

impl<T: Modulo> std::str::FromStr for ModInt<T> {
type Err = std::num::ParseIntError;
fn from_str(s: &str) -> Result<Self, Self::Err> {
let val = s.parse::<u32>()?;
Ok(ModInt::new(val))
}
}

impl<T: Modulo> From<usize> for ModInt<T> {
fn from(val: usize) -> ModInt<T> {
ModInt::new_unchecked((val % T::modulo() as usize) as u32)
}
}

impl<T: Modulo> From<u64> for ModInt<T> {
fn from(val: u64) -> ModInt<T> {
ModInt::new_unchecked((val % T::modulo() as u64) as u32)
}
}

impl<T: Modulo> From<i64> for ModInt<T> {
fn from(val: i64) -> ModInt<T> {
let m = T::modulo() as i64;
ModInt::new((val % m + m) as u32)
}
}

impl<T> ModInt<T> {
fn build(d: u32) -> Self {
ModInt(d, PhantomData)
}
pub fn zero() -> Self {
Self::build(0)
}
pub fn is_zero(&self) -> bool {
self.0 == 0
}
}

impl<T: Modulo> ModInt<T> {
pub fn new_unchecked(d: u32) -> Self {
Self::build(T::reduce(d as u64 * T::ini()))
}
pub fn new(d: u32) -> Self {
Self::new_unchecked(d % T::modulo())
}
pub fn one() -> Self {
Self::new_unchecked(1)
}
pub fn get(&self) -> u32 {
T::reduce(self.0 as u64)
}
pub fn pow(&self, mut n: u64) -> Self {
let mut t = Self::one();
let mut s = *self;
while n > 0 {
if n & 1 == 1 {
t *= s;
}
s *= s;
n >>= 1;
}
t
}
pub fn inv(&self) -> Self {
assert!(!self.is_zero());
self.pow((T::modulo() - 2) as u64)
}
}

pub fn mod_pow(mut r: u64, mut n: u64, m: u64) -> u64 {
let mut t = 1 % m;
while n > 0 {
if n & 1 == 1 {
t = t * r % m;
}
r = r * r % m;
n >>= 1;
}
t
}
}
// ---------- end ModInt ----------
// ---------- begin Precalc ----------
mod precalc {
use super::modint::*;
pub struct Precalc<T> {
inv: Vec<ModInt<T>>,
fact: Vec<ModInt<T>>,
ifact: Vec<ModInt<T>>,
}
impl<T: Modulo> Precalc<T> {
pub fn new(n: usize) -> Precalc<T> {
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) {
fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32);
}
ifact[n] = fact[n].inv();
if n > 0 {
inv[n] = ifact[n] * fact[n - 1];
}
for i in (1..n).rev() {
ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32);
inv[i] = ifact[i] * fact[i - 1];
}
Precalc {
inv: inv,
fact: fact,
ifact: ifact,
}
}
pub fn inv(&self, n: usize) -> ModInt<T> {
assert!(n > 0);
self.inv[n]
}
pub fn fact(&self, n: usize) -> ModInt<T> {
self.fact[n]
}
pub fn ifact(&self, n: usize) -> ModInt<T> {
self.ifact[n]
}
pub fn perm(&self, n: usize, k: usize) -> ModInt<T> {
if k > n {
return ModInt::zero();
}
self.fact[n] * self.ifact[n - k]
}
pub fn comb(&self, n: usize, k: usize) -> ModInt<T> {
if k > n {
return ModInt::zero();
}
self.fact[n] * self.ifact[k] * self.ifact[n - k]
}
}
}
// ---------- end Precalc ----------

use modint::*;

type M = ModInt<Mod1_000_000_007>;

// ---------- begin input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
(source = $s:expr,$($r:tt)*) => { let mut iter =$s.split_whitespace();
input_inner!{iter, $($r)*}
};
($($r:tt)*) => {
let s = {
let mut s = String::new();
s
};
let mut iter = s.split_whitespace();
input_inner!{iter, $($r)*}
};
}

macro_rules! input_inner {
($iter:expr) => {}; ($iter:expr, ) => {};
($iter:expr,$var:ident : $t:tt$($r:tt)*) => { let$var = read_value!($iter,$t);
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, $t)).collect::<Vec<_>>() }; ($iter:expr, chars) => {
read_value!($iter, String).chars().collect::<Vec<char>>() }; ($iter:expr, bytes) => {
read_value!($iter, String).bytes().collect::<Vec<u8>>() }; ($iter:expr, usize1) => {
read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => {$iter.next().unwrap().parse::<\$t>().expect("Parse error")
};
}
// ---------- end input macro ----------

use std::collections::*;

type Map<K, V> = BTreeMap<K, V>;
type Set<T> = BTreeSet<T>;
type Deque<T> = VecDeque<T>;

// l <= 1, n <= r
// a_i - i = a_j - j
// a_i != i
// l <= a_i <= r
//
// l - 1 <= a_1 - 1 <= r - 1
// l - n <= a_n - n <= r - n
//
// rが大きいorlが小さい時、a_i-i を等しくすることができ、これが最大
// どういう値？
// v = a_i - i
// v != 0
// v <= r - n
// v >= l - 1
// r > n だったら v = r - n とすればいいんじゃないか？
// a_i - i = r - n
// a_i = r - n + i
// サンプル2が合わないが
// 初手の変形間違ってる
// i < j で
// a_i + a_j = i + j
// a_i - i = -(a_i - j)
// a_i != i
// だいたい半分に分ける感じ？
// a_i > i と a_i < i の2種類で頑張る
// 愚直に計算する
// a_i - i の値を決め打つ
// 各iについてどっちに割り振れるかが決まる
// 割り振りかたをたしあげる
//
// naive なのはできた
//

fn run() {
input! {
t: usize,
}
let pc = precalc::Precalc::new(200000);
for (n, l, r) in ask {
let mut ans = M::zero();
for v in (1..=(r - 1)).rev() {
let mut cnt = [0; 4];
cnt[3] = (n.min(r - v) - (l + v).max(1) + 1).max(0);
cnt[1] = n.min(r - v) - cnt[3];
cnt[2] = n + 1 - (l + v).max(1) - cnt[3];
cnt[0] = n - cnt[1] - cnt[2] - cnt[3];
/*
for i in 1..=n {
let mut bit = 0;
if l - v <= i && i <= r - v {
bit |= 1;
}
if l + v <= i && i <= r + v {
bit |= 2;
}
cnt[bit] += 1;
}
*/
if cnt[0] > 0 {
continue;
}
let a = cnt[1];
let b = cnt[2];
let c = cnt[3];
let l = n / 2;
let r = n - l;
let mut way = M::zero();
if a <= l && b <= r {
way += pc.comb(c as usize, (l - a) as usize);
}
if l != r && a <= r && b <= l {
way += pc.comb(c as usize, (r - a) as usize);
}
if c == n {
ans += M::from(v) * way;
break;
} else {
ans += way;
}
}
println!("{}", ans);
}
}

fn main() {
run();
}


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