#![allow(unused_imports, non_snake_case)] #![allow(dead_code)] use crate::nums::{dot, matrix_mul, matrix_pow}; use crate::scanner::Scanner; modint!(); fn main() { let mut scan = Scanner::new(); let n = scan.read::(); let m = scan.read::(); let k = scan.read::(); let p = Z::new(scan.read::()); let q = Z::new(scan.read::()); let b = scan.readn::(n).map(|x| Z::new(x)); let mat = list! { list ! ( Z :: new ( 1 ) - p / q , p / q ) , list ! ( p / q , Z :: new ( 1 ) - p / q ) }; let mat_k = matrix_pow(&mat, k); let prob_from_tea_to_tea = mat_k[0][0]; let prob_from_kit_to_tea = mat_k[0][1]; let mut ret = Z::new(0); for i in 0..n { if i < m { ret += b[i] * prob_from_tea_to_tea; } else { ret += b[i] * prob_from_kit_to_tea; } } println!("{}", ret); } pub mod ext { pub mod range { use crate::independent::integer::Int; use std::cmp::{max, min}; use std::ops::{Bound, Range, RangeBounds, RangeInclusive}; pub trait RangeEx { fn width(&self) -> T; fn empty(&self) -> bool; fn contain_range(&self, inner: &Self) -> bool; fn separate_range(&self, other: &Self) -> bool; type ReturnRange; fn overlap(&self, other: &Self) -> Self::ReturnRange; } impl RangeEx for Range { fn width(&self) -> T { if self.empty() { T::zero() } else { self.end - self.start } } fn empty(&self) -> bool { !(self.start < self.end) } fn contain_range(&self, inner: &Self) -> bool { self.start <= inner.start && inner.end <= self.end } fn separate_range(&self, other: &Self) -> bool { self.end <= other.start || other.end <= self.start } type ReturnRange = Range; fn overlap(&self, other: &Self) -> Self::ReturnRange { let left = max(self.start, other.start); let right = min(self.end, other.end); left..right } } impl RangeEx for RangeInclusive { fn width(&self) -> T { if self.empty() { T::zero() } else { *self.end() - *self.start() + T::one() } } fn empty(&self) -> bool { !(self.start() <= self.end()) } fn contain_range(&self, inner: &Self) -> bool { self.start() <= inner.start() && inner.end() <= self.end() } fn separate_range(&self, other: &Self) -> bool { self.end() <= other.start() || other.end() <= self.start() } type ReturnRange = RangeInclusive; fn overlap(&self, other: &Self) -> Self::ReturnRange { let left = *max(self.start(), other.start()); let right = *min(self.end(), other.end()); left..=right } } pub trait IntRangeBounds: RangeBounds { #[doc = " inclusive"] fn lower_bound(&self, lower_bound: U) -> U { match self.start_bound() { Bound::Included(x) => max(lower_bound, *x), Bound::Excluded(x) => max(lower_bound, *x + U::one()), Bound::Unbounded => lower_bound, } } #[doc = " exclusive"] fn upper_bound(&self, upper_bound: U) -> U { match self.end_bound() { Bound::Included(x) => min(upper_bound, *x + U::one()), Bound::Excluded(x) => min(upper_bound, *x), Bound::Unbounded => upper_bound, } } fn to_harfopen(&self, lb: U, ub: U) -> Range { self.lower_bound(lb)..self.upper_bound(ub) } } impl IntRangeBounds for T where T: RangeBounds {} } } pub mod arraylist { use crate::{ext::range::IntRangeBounds, independent::integer::Int}; use std::fmt::Formatter; use std::iter::FromIterator; use std::ops::{Index, IndexMut, RangeBounds}; use std::slice::Iter; #[derive(Clone, PartialEq, Eq)] pub struct List { pub vec: Vec, } impl List { #[inline] pub fn new() -> List { List { vec: vec![] } } #[inline] pub fn init(init: T, n: i32) -> List where T: Clone, { List { vec: vec![init; n as usize], } } #[inline] pub fn from_vec(vec: Vec) -> List { List { vec } } #[inline] pub fn ilen(&self) -> i32 { self.vec.len() as i32 } #[inline] pub fn iter(&self) -> Iter<'_, T> { self.vec.iter() } #[inline] pub fn push(&mut self, item: T) { self.vec.push(item); } #[inline] pub fn sort(&mut self) where T: Ord, { self.vec.sort(); } #[inline] pub fn reverse(&mut self) { self.vec.reverse(); } #[inline] pub fn sort_by(&mut self, compare: F) where F: FnMut(&T, &T) -> std::cmp::Ordering, { self.vec.sort_by(compare) } #[inline] pub fn sort_by_key(&mut self, compare: F) where F: FnMut(&T) -> K, K: Ord, { self.vec.sort_by_key(compare) } #[inline] pub fn first(&self) -> Option<&T> { self.vec.first() } #[inline] pub fn last(&self) -> Option<&T> { self.vec.last() } #[inline] pub fn pop(&mut self) -> Option { self.vec.pop() } #[inline] pub fn swap(&mut self, i: i32, j: i32) { self.vec.swap(i as usize, j as usize); } #[inline] pub fn append(&mut self, mut other: Self) { self.vec.append(&mut other.vec); } #[inline] pub fn extend(&mut self, other: impl Iterator) { self.vec.extend(other); } #[inline] pub fn mirror(&self) -> std::iter::Cloned> where T: Clone, { self.iter().cloned() } #[inline] pub fn join(&self, sep: &str) -> String where T: std::fmt::Display, { self.iter() .map(|x| format!("{}", x)) .collect::>() .join(sep) } #[inline] pub fn map(&self, f: F) -> List where T: Clone, F: FnMut(T) -> B, { self.mirror().map(f).collect() } #[inline] pub fn filter

(&self, predicate: P) -> List where T: Clone, P: FnMut(&T) -> bool, { self.mirror().filter(predicate).collect() } #[inline] pub fn filter_map(&self, f: F) -> List where T: Clone, F: FnMut(T) -> Option, { self.mirror().filter_map(f).collect() } #[doc = " |acc, x| -> acc"] #[inline] pub fn fold(&self, init: B, f: F) -> B where T: Clone, F: FnMut(B, T) -> B, { self.mirror().fold(init, f) } #[inline] pub fn any

(&self, predicate: P) -> bool where P: FnMut(&T) -> bool, { self.iter().any(predicate) } #[inline] pub fn all

(&self, predicate: P) -> bool where P: FnMut(&T) -> bool, { self.iter().all(predicate) } #[inline] pub fn sum(&self) -> T where T: Int, { self.iter().cloned().fold(T::zero(), |acc, x| acc + x) } #[inline] pub fn enumerate(&self) -> List<(i32, T)> where T: Clone, { self.mirror() .enumerate() .map(|p| (p.0 as i32, p.1)) .collect() } #[inline] pub fn find

(&self, mut predicate: P) -> Option<&T> where P: FnMut(&T) -> bool, { self.iter().find(|x| predicate(*x)) } #[inline] pub fn index_of

(&self, mut predicate: P) -> Option where P: FnMut(&T) -> bool, { self.iter() .enumerate() .find(|&(_i, x)| predicate(x)) .map(|p| p.0 as i32) } #[inline] pub fn to>(&self) -> B where T: Clone, { self.mirror().collect() } #[inline] pub fn min(&self) -> Option<&T> where T: Ord, { self.iter().min() } #[inline] pub fn max(&self) -> Option<&T> where T: Ord, { self.iter().max() } #[inline] pub fn argmin(&self) -> Option where T: Ord, { let item = self.iter().min()?; self.iter() .enumerate() .find(|p| p.1 == item) .map(|p| p.0 as i32) } #[inline] pub fn argmax(&self) -> Option where T: Ord, { let item = self.iter().max()?; self.iter() .enumerate() .find(|p| p.1 == item) .map(|p| p.0 as i32) } #[inline] pub fn part(&self, range: U) -> List where T: Clone, U: RangeBounds, { List::from_vec( self.vec[range.lower_bound(0) as usize..range.upper_bound(self.ilen()) as usize] .to_vec(), ) } #[inline] pub fn first_exn(&self) -> &T { self.first().unwrap() } #[inline] pub fn last_exn(&self) -> &T { self.last().unwrap() } #[inline] pub fn pop_exn(&mut self) -> T { self.pop().unwrap() } #[inline] pub fn min_exn(&self) -> &T where T: Ord, { self.min().unwrap() } #[inline] pub fn max_exn(&self) -> &T where T: Ord, { self.max().unwrap() } #[inline] pub fn argmin_exn(&self) -> i32 where T: Ord, { self.argmin().unwrap() } #[inline] pub fn argmax_exn(&self) -> i32 where T: Ord, { self.argmax().unwrap() } #[inline] pub fn find_exn

(&self, predicate: P) -> &T where P: FnMut(&T) -> bool, { self.find(predicate).unwrap() } #[inline] pub fn index_of_exn

(&self, predicate: P) -> i32 where P: FnMut(&T) -> bool, { self.index_of(predicate).unwrap() } } impl Index for List { type Output = T; #[inline] fn index(&self, index: i32) -> &Self::Output { if cfg!(debug_assertions) { self.vec.index(index as usize) } else { unsafe { self.vec.get_unchecked(index as usize) } } } } impl IndexMut for List { #[inline] fn index_mut(&mut self, index: i32) -> &mut Self::Output { if cfg!(debug_assertions) { self.vec.index_mut(index as usize) } else { unsafe { self.vec.get_unchecked_mut(index as usize) } } } } impl FromIterator for List { fn from_iter>(iter: U) -> Self { let mut vec = vec![]; for i in iter { vec.push(i); } List { vec } } } impl IntoIterator for List { type Item = T; type IntoIter = std::vec::IntoIter; fn into_iter(self) -> std::vec::IntoIter { self.vec.into_iter() } } impl<'a, T> IntoIterator for &'a List { type Item = &'a T; type IntoIter = Iter<'a, T>; fn into_iter(self) -> Iter<'a, T> { self.vec.iter() } } impl std::fmt::Display for List { fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result { write!( f, "{}", self.iter() .map(|x| format!("{}", x)) .collect::>() .join(" ") ) } } impl std::fmt::Debug for List { fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result { write!( f, "[{}]", self.iter() .map(|x| format!("{:?}", x)) .collect::>() .join(", ") ) } } impl From> for List { fn from(vec: Vec) -> Self { Self::from_vec(vec) } } impl From<&[T]> for List { fn from(slice: &[T]) -> Self { slice.iter().cloned().collect() } } #[macro_export] macro_rules ! list { ( ) => { $ crate :: arraylist :: List :: new ( ) } ; ( $ ( $ v : expr ) ,* ) => { $ crate :: arraylist :: List :: from_vec ( vec ! [ $ ( $ v ) ,* ] ) } ; ( $ v : expr ; $ a : expr ) => { $ crate :: arraylist :: List :: init ( $ v , $ a ) } ; ( $ v : expr ; $ a : expr ; $ ( $ rest : expr ) ;+ ) => { $ crate :: arraylist :: List :: init ( list ! ( $ v ; $ ( $ rest ) ;+ ) , $ a ) } ; } } pub mod modulo { use crate::independent::integer::Int; use std::marker::PhantomData; use std::ops::*; #[derive(Debug, PartialEq, Eq, Copy, Clone, Hash, PartialOrd, Ord)] pub struct ModInt(pub i64, PhantomData<*const T>); impl ModInt { pub fn new(a: U) -> ModInt { let x = a.to_i64(); if x < 0 { ModInt::raw(x % T::M + T::M) } else if x < T::M { ModInt::raw(x) } else { ModInt::raw(x % T::M) } } pub fn pow(self, x: U) -> Self { let mut n = x.to_i64(); let mut a = self; let mut res = Self::raw(1); while n > 0 { if n & 1 == 1 { res *= a; } a = a * a; n >>= 1; } res } pub fn inv(self) -> Self { self.pow(T::M - 2) } #[inline] fn raw(x: i64) -> ModInt { ModInt(x, PhantomData) } } pub trait ConstValue: PartialEq + Eq + Copy + Clone + std::hash::Hash + Ord { const M: i64; } impl std::fmt::Display for ModInt { fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result { write!(f, "{}", self.0) } } macro_rules ! impl_from_for_modint { ( $ ( $ tpe : ident ) ,* ) => { $ ( impl < T : ConstValue > From <$ tpe > for ModInt < T > { fn from ( n : $ tpe ) -> Self { Self :: new ( n ) } } ) * } ; } impl_from_for_modint!(u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, usize, isize); impl Add for ModInt { type Output = ModInt; fn add(self, other: ModInt) -> ModInt { let mut ret = self.0 + other.0; if ret >= T::M { ret -= T::M; } Self::raw(ret) } } impl AddAssign for ModInt { fn add_assign(&mut self, other: Self) { *self = self.add(other); } } impl Sub for ModInt { type Output = ModInt; fn sub(self, other: ModInt) -> ModInt { let mut ret = self.0 + T::M - other.0; if ret >= T::M { ret -= T::M } Self::raw(ret) } } impl SubAssign for ModInt { fn sub_assign(&mut self, other: Self) { *self = self.sub(other); } } impl Mul for ModInt { type Output = ModInt; fn mul(self, other: ModInt) -> ModInt { Self::raw(self.0 * other.0 % T::M) } } impl MulAssign for ModInt { fn mul_assign(&mut self, other: Self) { *self = self.mul(other); } } impl Div for ModInt { type Output = ModInt; fn div(self, other: ModInt) -> ModInt { self * other.inv() } } impl DivAssign for ModInt { fn div_assign(&mut self, other: Self) { *self = self.div(other); } } impl Rem for ModInt { type Output = ModInt; fn rem(self, other: ModInt) -> ModInt { Self::raw(self.0 % other.0) } } #[macro_export] macro_rules! modint { ( ) => { modint!(1000000007); }; ( $ m : expr ) => { #[derive(Debug, PartialEq, Eq, Copy, Clone, Hash, PartialOrd, Ord)] pub enum __M {} impl $crate::modulo::ConstValue for __M { const M: i64 = $m; } #[allow(dead_code)] type Z = $crate::modulo::ModInt<__M>; }; } macro_rules ! impl_integer_functions { ( $ ( $ tofn : ident , $ fromfn : ident , $ tpe : ident ) ,* ) => { $ ( fn $ tofn ( & self ) -> $ tpe { self . 0 as $ tpe } fn $ fromfn ( x : $ tpe ) -> Self { Self :: new ( x ) } ) * } ; } impl Int for ModInt { impl_integer_functions!( to_u8, from_u8, u8, to_u16, from_u16, u16, to_u32, from_u32, u32, to_u64, from_u64, u64, to_u128, from_u128, u128, to_i8, from_i8, i8, to_i16, from_i16, i16, to_i32, from_i32, i32, to_i64, from_i64, i64, to_i128, from_i128, i128, to_usize, from_usize, usize, to_isize, from_isize, isize ); fn zero() -> Self { Self::new(0) } fn one() -> Self { Self::new(1) } } } pub mod scanner { use crate::arraylist::List; use std::io::{stdin, BufReader, Bytes, Read, Stdin}; use std::str::FromStr; pub struct Scanner { buf: Bytes>, } impl Scanner { pub fn new() -> Scanner { Scanner { buf: BufReader::new(stdin()).bytes(), } } pub fn read_next(&mut self) -> Option { let token = self .buf .by_ref() .map(|c| c.unwrap() as char) .skip_while(|c| c.is_whitespace()) .take_while(|c| !c.is_whitespace()) .collect::(); token.parse::().ok() } pub fn read(&mut self) -> T { self.read_next().unwrap() } pub fn readn(&mut self, n: i32) -> List { (0..n).map(|_| self.read::()).collect() } pub fn chars(&mut self) -> List { self.read::().chars().collect() } } } pub mod nums { use crate::{arraylist::List, independent::integer::Int}; pub fn gcd(a: i64, b: i64) -> i64 { if b == 0 { a } else { gcd(b, a % b) } } pub fn lcm(a: i64, b: i64) -> i64 { a / gcd(a, b) * b } pub fn extgcd(a: i64, b: i64) -> (i64, i64, i64) { if b == 0 { (a, 1, 0) } else { let (gcd, x, y) = extgcd(b, a % b); (gcd, y, x - (a / b) * y) } } pub fn modinv_extgcd(m: i64, a_: i64) -> i64 { let mut a = a_; let mut b = m; let mut u = 1; let mut v = 0; while b != 0 { let t = a / b; a -= t * b; std::mem::swap(&mut a, &mut b); u -= t * v; std::mem::swap(&mut u, &mut v); } u %= m; if u < 0 { u += m }; u } pub fn dot(a: &List, b: &List) -> T { let mut c = T::zero(); for i in 0..a.ilen() { c += a[i] * b[i]; } c } pub fn cross(a: &List, b: &List) -> T { a[0] * b[1] - a[1] * b[0] } pub fn matrix_mul(a: &List>, b: &List>) -> List> { let mut c = List::init(List::init(T::zero(), b[0].ilen()), a.ilen()); for i in 0..a.ilen() { for k in 0..b.ilen() { for j in 0..b[0].ilen() { c[i][j] = c[i][j] + a[i][k] * b[k][j]; } } } c } pub fn matrix_pow(a_: &List>, mut n: i64) -> List> { let mut a = a_.clone(); let mut b = List::init(List::init(T::zero(), a.ilen()), a.ilen()); for i in 0..a.ilen() { b[i][i] = T::one(); } while n > 0 { if n & 1 == 1 { b = matrix_mul(&b, &a); } a = matrix_mul(&a, &a); n >>= 1; } b } pub fn ceil_div(x: i64, y: i64) -> i64 { (x + y - 1) / y } } pub mod independent { pub mod integer { pub trait Int: std::ops::Add + std::ops::Sub + std::ops::Mul + std::ops::Div + std::ops::Rem + std::ops::AddAssign + std::ops::SubAssign + std::ops::MulAssign + std::ops::DivAssign + std::hash::Hash + PartialEq + Eq + PartialOrd + Ord + Copy { fn to_u8(&self) -> u8; fn to_u16(&self) -> u16; fn to_u32(&self) -> u32; fn to_u64(&self) -> u64; fn to_u128(&self) -> u128; fn to_i8(&self) -> i8; fn to_i16(&self) -> i16; fn to_i32(&self) -> i32; fn to_i64(&self) -> i64; fn to_i128(&self) -> i128; fn to_usize(&self) -> usize; fn to_isize(&self) -> isize; fn from_u8(x: u8) -> Self; fn from_u16(x: u16) -> Self; fn from_u32(x: u32) -> Self; fn from_u64(x: u64) -> Self; fn from_u128(x: u128) -> Self; fn from_i8(x: i8) -> Self; fn from_i16(x: i16) -> Self; fn from_i32(x: i32) -> Self; fn from_i64(x: i64) -> Self; fn from_i128(x: i128) -> Self; fn from_usize(x: usize) -> Self; fn from_isize(x: isize) -> Self; fn zero() -> Self; fn one() -> Self; fn next(&self) -> Self { *self + Self::one() } } macro_rules ! impl_integer_functions { ( $ selftpe : ident , $ ( $ tofn : ident , $ fromfn : ident , $ tpe : ident ) ,* ) => { $ ( fn $ tofn ( & self ) -> $ tpe { * self as $ tpe } fn $ fromfn ( x : $ tpe ) -> Self { x as $ selftpe } ) * } ; } macro_rules ! impl_integer { ( $ ( $ tpe : ident ) ,* ) => { $ ( impl Int for $ tpe { impl_integer_functions ! ( $ tpe , to_u8 , from_u8 , u8 , to_u16 , from_u16 , u16 , to_u32 , from_u32 , u32 , to_u64 , from_u64 , u64 , to_u128 , from_u128 , u128 , to_i8 , from_i8 , i8 , to_i16 , from_i16 , i16 , to_i32 , from_i32 , i32 , to_i64 , from_i64 , i64 , to_i128 , from_i128 , i128 , to_usize , from_usize , usize , to_isize , from_isize , isize ) ; fn zero ( ) -> Self { 0 } fn one ( ) -> Self { 1 } } ) * } ; } impl_integer!(u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, usize, isize); } }