fn getline() -> String { let mut ret = String::new(); std::io::stdin().read_line(&mut ret).ok().unwrap(); ret } /// Verified by https://atcoder.jp/contests/arc093/submissions/3968098 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>> 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 ::std::fmt::Debug 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

; // Depends on MInt.rs // Verified by: https://atcoder.jp/contests/abc199/submissions/22259436 fn squmul(a: &[Vec], b: &[Vec]) -> Vec> { let n = a.len(); let mut ret = vec![vec![MInt::new(0); n]; n]; for i in 0..n { for j in 0..n { for k in 0..n { ret[i][k] += a[i][j] * b[j][k]; } } } ret } fn squpow(a: &[Vec], mut e: i64) -> Vec> { let n = a.len(); let mut sum = vec![vec![MInt::new(0); n]; n]; for i in 0..n { sum[i][i] = 1.into(); } let mut cur = a.to_vec(); while e > 0 { if e % 2 == 1 { sum = squmul(&sum, &cur); } cur = squmul(&cur, &cur); e /= 2; } sum } fn main() { let ints = getline().trim().split_whitespace() .map(|s| s.parse::().unwrap()).collect::>(); let [a, b, c, d, e, n] = ints[..] else { panic!() }; let a = MInt::new(a + MOD); let b = MInt::new(b + MOD); let c = MInt::new(c + MOD); let d = MInt::new(d + MOD); let e = MInt::new(e + MOD); let mut trans = vec![vec![MInt::new(0); 4]; 4]; trans[1][0] += 1; trans[0][1] = d; trans[1][1] = c; trans[3][1] = e; trans[2][2] += 1; trans[0][2] += 1; trans[3][3] += 1; let mut u = vec![MInt::new(0); 4]; u[0] = a.into(); u[1] = b.into(); u[3] = 1.into(); let apw = squpow(&trans, n + 1); let mut ans = MInt::new(0); for i in 0..4 { ans += u[i] * apw[i][2]; } println!("{ans}"); }