use std::cmp::*; use std::io::Read; fn get_word() -> String { let stdin = std::io::stdin(); let mut stdin=stdin.lock(); let mut u8b: [u8; 1] = [0]; loop { let mut buf: Vec = Vec::with_capacity(16); loop { let res = stdin.read(&mut u8b); if res.unwrap_or(0) == 0 || u8b[0] <= b' ' { break; } else { buf.push(u8b[0]); } } if buf.len() >= 1 { let ret = String::from_utf8(buf).unwrap(); return ret; } } } fn get() -> T { get_word().parse().ok().unwrap() } /// Verified by https://atcoder.jp/contests/abc198/submissions/21774342 mod mod_int { use std::ops::*; pub trait Mod: Copy { fn m() -> i64; } #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)] pub struct ModInt { pub x: i64, phantom: ::std::marker::PhantomData } impl ModInt { // x >= 0 pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) } fn new_internal(x: i64) -> Self { ModInt { x: x, phantom: ::std::marker::PhantomData } } pub fn pow(self, mut e: i64) -> Self { debug_assert!(e >= 0); let mut sum = ModInt::new_internal(1); let mut cur = self; while e > 0 { if e % 2 != 0 { sum *= cur; } cur *= cur; e /= 2; } sum } #[allow(dead_code)] pub fn inv(self) -> Self { self.pow(M::m() - 2) } } impl Default for ModInt { fn default() -> Self { Self::new_internal(0) } } impl>> Add for ModInt { type Output = Self; fn add(self, other: T) -> Self { let other = other.into(); let mut sum = self.x + other.x; if sum >= M::m() { sum -= M::m(); } ModInt::new_internal(sum) } } impl>> Sub for ModInt { type Output = Self; fn sub(self, other: T) -> Self { let other = other.into(); let mut sum = self.x - other.x; if sum < 0 { sum += M::m(); } ModInt::new_internal(sum) } } impl>> Mul for ModInt { type Output = Self; fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) } } impl>> AddAssign for ModInt { fn add_assign(&mut self, other: T) { *self = *self + other; } } impl>> SubAssign for ModInt { fn sub_assign(&mut self, other: T) { *self = *self - other; } } impl>> MulAssign for ModInt { fn mul_assign(&mut self, other: T) { *self = *self * other; } } impl Neg for ModInt { type Output = Self; fn neg(self) -> Self { ModInt::new(0) - self } } impl ::std::fmt::Display for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { self.x.fmt(f) } } impl From for ModInt { fn from(x: i64) -> Self { Self::new(x) } } } // mod mod_int macro_rules! define_mod { ($struct_name: ident, $modulo: expr) => { #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)] struct $struct_name {} impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } } } } const MOD: i64 = 1_000_000_007; define_mod!(P, MOD); type MInt = mod_int::ModInt

; // https://yukicoder.me/problems/no/2367 (3.5) // 以下のような部分問題を解けば良い: // レベル K のガスケットの周り  i 箇所が j 色で塗られているとして、ガスケットを塗る方法は何通り? // これは DP でできて O(N) 時間。 fn main() { let k: i64 = get(); let n: i64 = get(); let mut dp = [MInt::new(0); 4]; let mut dp2 = [MInt::new(0); 4]; let mut dp3 = MInt::new(0); dp[0] += n; dp[1] += n - 1; dp[2] += max(n - 2, 0); dp[3] += max(n - 3, 0); dp2[2] += n - 1; dp2[3] += max(n - 2, 0); dp3 += n - 1; for i in 0..k { let mut ep = [MInt::new(0); 4]; let mut ep2 = [MInt::new(0); 4]; ep[0] = dp[1].pow(3) * n; ep[1] = dp2[2].pow(2) * dp[1] + dp[2].pow(2) * dp[1] * (n - 1); ep[2] = dp2[2] * dp2[3] * dp[2] * 2 + dp[2].pow(2) * dp[3] * max(n - 2, 0); ep[3] = dp2[3].pow(2) * dp[3] * 3 + dp[3].pow(3) * max(n - 3, 0); ep2[2] = dp2[2].pow(2) * dp3 + dp[2].pow(2) * dp2[3] * (n - 1); ep2[3] = dp2[3].pow(2) * dp3 + dp2[3].pow(3) + dp2[3] * dp[3].pow(2) * max(n - 2, 0); let ep3 = dp3.pow(3) + dp2[3].pow(3) * (n - 1); dp = ep; dp2 = ep2; dp3 = ep3; } println!("{}", dp[0]); }