#![allow(unused_macros)] #![allow(dead_code)] #![allow(unused_imports)] use crate::lib::{Scanner, ModInt}; // use itertools::Itertools; use std::collections::*; use std::process::exit; const U_INF: usize = 1 << 60; const I_INF: isize = 1 << 60; fn main() { let mut sc = Scanner::new(); let n = sc.next_isize(); let mut s = sc.next_isize(); let k = sc.next_isize(); s -= k * (n - 1) * n / 2; if s < 0 { println!("0"); exit(0); } // s円をn人に分ける let mut dp = vec![vec![ModInt::new(0); s as usize + 1]; n as usize + 1]; dp[0][0] = ModInt::new(1); for i in 0..=n as usize { for j in 0..=s as usize { let mut tmp = ModInt::new(0); if i != 0 { tmp += dp[i - 1][j]; } if j >= i { tmp += dp[i][j - i]; } dp[i][j] = tmp; } } println!("{}", dp[n as usize][s as usize]); } pub mod lib { pub const MOD: isize = 1000000007; // pub const MOD: isize = 998244353; /// 常に設定したModを取り続ける正整数型 #[derive(Debug, Copy, Clone, Ord, PartialOrd, Eq, PartialEq)] pub struct ModInt { /// 保持する値 value: isize, } impl ModInt { /// isizeを受け取り、ModIntに変換する pub fn new(n: isize) -> Self { let mut value = n % MOD; if value < 0 { value += MOD; } Self { value } } /// べき乗計算関数 /// 二分累乗法を用いるため、計算量はO(log n) pub fn pow(self, n: usize) -> Self { match n { 0 => ModInt::new(1), 1 => self, n if n % 2 == 0 => (self * self).pow(n / 2), _ => self * self.pow(n - 1), } } /// 逆元を返す /// フェルマーの小定理より、べき乗を用いて計算するため、計算量はO(log MOD) pub fn inv(self) -> Self { self.pow((MOD - 2) as usize) } } impl std::fmt::Display for ModInt { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { write!(f, "{}", self.value) } } impl From for ModInt { fn from(n: usize) -> Self { Self::new(n as isize) } } impl From for ModInt { fn from(n: u64) -> Self { Self::new(n as isize) } } impl From for ModInt { fn from(n: u32) -> Self { Self::new(n as isize) } } impl From for ModInt { fn from(n: u16) -> Self { Self::new(n as isize) } } impl From for ModInt { fn from(n: u8) -> Self { Self::new(n as isize) } } impl From for ModInt { fn from(n: isize) -> Self { Self::new(n) } } impl From for ModInt { fn from(n: i64) -> Self { Self::new(n as isize) } } impl From for ModInt { fn from(n: i32) -> Self { Self::new(n as isize) } } impl From for ModInt { fn from(n: i16) -> Self { Self::new(n as isize) } } impl From for ModInt { fn from(n: i8) -> Self { Self::new(n as isize) } } impl std::ops::Add for ModInt { type Output = Self; fn add(self, rhs: Self) -> Self::Output { let mut tmp = self.value + rhs.value; if tmp >= MOD { tmp %= MOD; } Self { value: tmp } } } impl std::ops::AddAssign for ModInt { fn add_assign(&mut self, rhs: Self) { *self = *self + rhs } } impl std::ops::Sub for ModInt { type Output = ModInt; fn sub(self, rhs: Self) -> Self::Output { let mut tmp = self.value; if tmp < rhs.value { tmp += MOD; } tmp -= rhs.value; if tmp >= MOD { tmp %= MOD; } Self { value: tmp } } } impl std::ops::SubAssign for ModInt { fn sub_assign(&mut self, rhs: Self) { *self = *self - rhs; } } impl std::ops::Mul for ModInt { type Output = ModInt; fn mul(self, rhs: Self) -> Self::Output { let mut tmp = self.value * rhs.value; if tmp >= MOD { tmp %= MOD; } Self { value: tmp } } } impl std::ops::MulAssign for ModInt { fn mul_assign(&mut self, rhs: Self) { *self = *self * rhs; } } impl std::ops::Div for ModInt { type Output = ModInt; fn div(self, rhs: Self) -> Self::Output { self * rhs.inv() } } impl std::ops::DivAssign for ModInt { fn div_assign(&mut self, rhs: Self) { *self = *self / rhs; } } /// 二項係数を高速に計算するテーブルを作成する /// 構築 O(N) /// クエリ O(1) /// メモリ O(N) pub struct CombTable { fac: Vec, f_inv: Vec, } impl CombTable { /// O(N)で構築 pub fn new(n: usize) -> Self { let mut fac = vec![ModInt::new(1); n + 1]; let mut f_inv = vec![ModInt::new(1); n + 1]; let mut inv = vec![ModInt::new(1); n + 1]; inv[0] = ModInt::new(0); for i in 2..=n { fac[i] = fac[i - 1] * i.into(); inv[i] = ModInt::new(MOD) - inv[(MOD % i as isize) as usize] * ModInt::new(MOD / i as isize); f_inv[i] = f_inv[i - 1] * inv[i]; } Self { fac, f_inv } } /// nCkをO(1)で計算 pub fn comb(&self, n: usize, k: usize) -> ModInt { if n < k || n * k == 0 { return ModInt::new(0); } self.fac[n] * (self.f_inv[k] * self.f_inv[n - k]) } } pub struct Scanner { buf: std::collections::VecDeque, } impl Scanner { pub fn new() -> Self { Self { buf: std::collections::VecDeque::new(), } } fn scan_line(&mut self) { let mut flag = 0; while self.buf.is_empty() { let mut s = String::new(); std::io::stdin().read_line(&mut s).unwrap(); let mut iter = s.split_whitespace().peekable(); if iter.peek().is_none() { if flag >= 5 { panic!("There is no input!"); } flag += 1; continue; } for si in iter { self.buf.push_back(si.to_string()); } } } pub fn next(&mut self) -> T { self.scan_line(); self.buf .pop_front() .unwrap() .parse() .unwrap_or_else(|_| panic!("Couldn't parse!")) } pub fn next_usize(&mut self) -> usize { self.next() } pub fn next_isize(&mut self) -> isize { self.next() } pub fn next_chars(&mut self) -> Vec { self.next::().chars().collect() } pub fn next_string(&mut self) -> String { self.next() } pub fn next_char(&mut self) -> char { self.next() } pub fn next_float(&mut self) -> f64 { self.next() } } }