Problem:
Score : 400 points

Problem Statement

Takahashi will play a game using a piece on an array of squares numbered 1, 2, \cdots, N. Square i has an integer C_i written on it. Also, he is given a permutation of 1, 2, \cdots, N: P_1, P_2, \cdots, P_N.

Now, he will choose one square and place the piece on that square. Then, he will make the following move some number of times between 1 and K (inclusive):

In one move, if the piece is now on Square i (1 \leq i \leq N), move it to Square P_i. Here, his score increases by C_{P_i}.

Help him by finding the maximum possible score at the end of the game. (The score is 0 at the beginning of the game.)

Constraints

2 \leq N \leq 5000

1 \leq K \leq 10^9

1 \leq P_i \leq N

P_i \neq i

P_1, P_2, \cdots, P_N are all different.

-10^9 \leq C_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
P_1 P_2 \cdots P_N
C_1 C_2 \cdots C_N

Output

Print the maximum possible score at the end of the game.

Sample Input 1

5 2
2 4 5 1 3
3 4 -10 -8 8

Sample Output 1

8

When we start at some square of our choice and make at most two moves, we have the following options:

If we start at Square 1, making one move sends the piece to Square 2, after which the score is 4. Making another move sends the piece to Square 4, after which the score is 4 + (-8) = -4.

If we start at Square 2, making one move sends the piece to Square 4, after which the score is -8. Making another move sends the piece to Square 1, after which the score is -8 + 3 = -5.

If we start at Square 3, making one move sends the piece to Square 5, after which the score is 8. Making another move sends the piece to Square 3, after which the score is 8 + (-10) = -2.

If we start at Square 4, making one move sends the piece to Square 1, after which the score is 3. Making another move sends the piece to Square 2, after which the score is 3 + 4 = 7.

If we start at Square 5, making one move sends the piece to Square 3, after which the score is -10. Making another move sends the piece to Square 5, after which the score is -10 + 8 = -2.

The maximum score achieved is 8.

Sample Input 2

2 3
2 1
10 -7

Sample Output 2

13

Sample Input 3

3 3
3 1 2
-1000 -2000 -3000

Sample Output 3

-1000

We have to make at least one move.

Sample Input 4

10 58
9 1 6 7 8 4 3 2 10 5
695279662 988782657 -119067776 382975538 -151885171 -177220596 -169777795 37619092 389386780 980092719

Sample Output 4

29507023469

The absolute value of the answer may be enormous.

Solution in Rust (1.42.0) (judge verdict: Time Limit Exceeded)

// SNIPPET read
pub trait Readable {
    type Output;
    const WORD_COUNT: usize;
    fn read_words(words: &[&str]) -> Result<Self::Output, String>;
}
#[macro_export]
macro_rules! readable {
    ( $t:ty, $words_count:expr, |$words:ident| $read_words:expr ) => {
        impl Readable for $t {
            type Output = $t;
            const WORD_COUNT: usize = $words_count;
            fn read_words($words: &[&str]) -> Result<$t, String> {
                Ok($read_words)
            }
        }
    };
}
readable!((), 1, |_ss| ());
readable!(String, 1, |ss| ss[0].to_string());
impl Readable for char {
    type Output = char;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<char, String> {
        let chars: Vec<char> = words[0].chars().collect();
        if chars.len() == 1 {
            Ok(chars[0])
        } else {
            Err(format!("cannot parse `{}` as a char", words[0]))
        }
    }
}
pub struct Chars();
impl Readable for Chars {
    type Output = Vec<char>;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Vec<char>, String> {
        Ok(words[0].chars().collect())
    }
}
pub struct Bytes();
impl Readable for Bytes {
    type Output = Vec<u8>;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Vec<u8>, String> {
        Ok(words[0].bytes().collect())
    }
}
impl Readable for i8 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<i8, String> {
        use std::str::FromStr;
        i8::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i8", words[0])
        })
    }
}
impl Readable for u8 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<u8, String> {
        use std::str::FromStr;
        u8::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u8", words[0])
        })
    }
}
impl Readable for i16 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<i16, String> {
        use std::str::FromStr;
        i16::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i16", words[0])
        })
    }
}
impl Readable for u16 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<u16, String> {
        use std::str::FromStr;
        u16::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u16", words[0])
        })
    }
}
impl Readable for i32 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<i32, String> {
        use std::str::FromStr;
        i32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i32", words[0])
        })
    }
}
impl Readable for u32 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<u32, String> {
        use std::str::FromStr;
        u32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u32", words[0])
        })
    }
}
impl Readable for i64 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<i64, String> {
        use std::str::FromStr;
        i64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i64", words[0])
        })
    }
}
impl Readable for u64 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<u64, String> {
        use std::str::FromStr;
        u64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u64", words[0])
        })
    }
}
impl Readable for i128 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<i128, String> {
        use std::str::FromStr;
        i128::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i64", words[0])
        })
    }
}
impl Readable for u128 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<u128, String> {
        use std::str::FromStr;
        u128::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u64", words[0])
        })
    }
}
impl Readable for isize {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<isize, String> {
        use std::str::FromStr;
        <isize>::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as isize", words[0])
        })
    }
}
impl Readable for usize {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<usize, String> {
        use std::str::FromStr;
        <usize>::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as usize", words[0])
        })
    }
}
impl Readable for f32 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<f32, String> {
        use std::str::FromStr;
        f32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as f32", words[0])
        })
    }
}
impl Readable for f64 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<f64, String> {
        use std::str::FromStr;
        f64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as f64", words[0])
        })
    }
}
#[allow(non_camel_case_types)]
pub struct u8_;
impl Readable for u8_ {
    type Output = u8;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u8::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u16_;
impl Readable for u16_ {
    type Output = u16;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u16::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u32_;
impl Readable for u32_ {
    type Output = u32;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u32::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u64_;
impl Readable for u64_ {
    type Output = u64;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u64::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct usize_;
impl Readable for usize_ {
    type Output = usize;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        <usize>::read_words(words).map(|n| n-1)
    }
}
impl<T1: Readable, T2: Readable> Readable for (T1, T2) {
    type Output = (T1::Output, T2::Output);
    const WORD_COUNT: usize = T1::WORD_COUNT + T2::WORD_COUNT;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let mut start = 0;
        let count1 = T1::WORD_COUNT;
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let val2 = T2::read_words(&words[start..])?;
        Ok((val1, val2))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable> Readable for (T1, T2, T3) {
    type Output = (T1::Output, T2::Output, T3::Output);
    const WORD_COUNT: usize = T1::WORD_COUNT + T2::WORD_COUNT + T3::WORD_COUNT;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let mut start = 0;
        let count1 = T1::WORD_COUNT;
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::WORD_COUNT;
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let val3 = T3::read_words(&words[start..])?;
        Ok((val1, val2, val3))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable> Readable for (T1, T2, T3, T4) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output);
    const WORD_COUNT: usize = T1::WORD_COUNT + T2::WORD_COUNT + T3::WORD_COUNT + T4::WORD_COUNT;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let mut start = 0;
        let count1 = T1::WORD_COUNT;
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::WORD_COUNT;
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::WORD_COUNT;
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let val4 = T4::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, T5: Readable> Readable for (T1, T2, T3, T4, T5) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output, T5::Output);
    const WORD_COUNT: usize = T1::WORD_COUNT + T2::WORD_COUNT + T3::WORD_COUNT + T4::WORD_COUNT + T5::WORD_COUNT;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let mut start = 0;
        let count1 = T1::WORD_COUNT;
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::WORD_COUNT;
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::WORD_COUNT;
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let count4 = T4::WORD_COUNT;
        let val4 = T4::read_words(&words[start .. start+count4])?;
        start += count4;
        let val5 = T5::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4, val5))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, T5: Readable, T6: Readable> Readable for (T1, T2, T3, T4, T5, T6) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output, T5::Output, T6::Output);
    const WORD_COUNT: usize = T1::WORD_COUNT + T2::WORD_COUNT + T3::WORD_COUNT + T4::WORD_COUNT + T5::WORD_COUNT + T6::WORD_COUNT;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let mut start = 0;
        let count1 = T1::WORD_COUNT;
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::WORD_COUNT;
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::WORD_COUNT;
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let count4 = T4::WORD_COUNT;
        let val4 = T4::read_words(&words[start .. start+count4])?;
        start += count4;
        let count5 = T5::WORD_COUNT;
        let val5 = T5::read_words(&words[start .. start+count5])?;
        start += count5;
        let val6 = T6::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4, val5, val6))
    }
}
impl<T: Readable> Readable for [T; 2] {
    type Output = [T::Output; 2];
    const WORD_COUNT: usize = T::WORD_COUNT * 2;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let val1 = T::read_words(&words[T::WORD_COUNT*0 .. T::WORD_COUNT*1])?;
        let val2 = T::read_words(&words[T::WORD_COUNT*1 .. T::WORD_COUNT*2])?;
        Ok([val1, val2])
    }
}
impl<T: Readable> Readable for [T; 3] {
    type Output = [T::Output; 3];
    const WORD_COUNT: usize = T::WORD_COUNT * 3;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let val1 = T::read_words(&words[T::WORD_COUNT*0 .. T::WORD_COUNT*1])?;
        let val2 = T::read_words(&words[T::WORD_COUNT*1 .. T::WORD_COUNT*2])?;
        let val3 = T::read_words(&words[T::WORD_COUNT*2 .. T::WORD_COUNT*3])?;
        Ok([val1, val2, val3])
    }
}
impl<T: Readable> Readable for [T; 4] {
    type Output = [T::Output; 4];
    const WORD_COUNT: usize = T::WORD_COUNT * 4;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let val1 = T::read_words(&words[T::WORD_COUNT*0 .. T::WORD_COUNT*1])?;
        let val2 = T::read_words(&words[T::WORD_COUNT*1 .. T::WORD_COUNT*2])?;
        let val3 = T::read_words(&words[T::WORD_COUNT*2 .. T::WORD_COUNT*3])?;
        let val4 = T::read_words(&words[T::WORD_COUNT*3 .. T::WORD_COUNT*4])?;
        Ok([val1, val2, val3, val4])
    }
}
impl<T: Readable> Readable for [T; 5] {
    type Output = [T::Output; 5];
    const WORD_COUNT: usize = T::WORD_COUNT * 5;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let val1 = T::read_words(&words[T::WORD_COUNT*0 .. T::WORD_COUNT*1])?;
        let val2 = T::read_words(&words[T::WORD_COUNT*1 .. T::WORD_COUNT*2])?;
        let val3 = T::read_words(&words[T::WORD_COUNT*2 .. T::WORD_COUNT*3])?;
        let val4 = T::read_words(&words[T::WORD_COUNT*3 .. T::WORD_COUNT*4])?;
        let val5 = T::read_words(&words[T::WORD_COUNT*4 .. T::WORD_COUNT*5])?;
        Ok([val1, val2, val3, val4, val5])
    }
}
impl<T: Readable> Readable for [T; 6] {
    type Output = [T::Output; 6];
    const WORD_COUNT: usize = T::WORD_COUNT * 6;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let val1 = T::read_words(&words[T::WORD_COUNT*0 .. T::WORD_COUNT*1])?;
        let val2 = T::read_words(&words[T::WORD_COUNT*1 .. T::WORD_COUNT*2])?;
        let val3 = T::read_words(&words[T::WORD_COUNT*2 .. T::WORD_COUNT*3])?;
        let val4 = T::read_words(&words[T::WORD_COUNT*3 .. T::WORD_COUNT*4])?;
        let val5 = T::read_words(&words[T::WORD_COUNT*4 .. T::WORD_COUNT*5])?;
        let val6 = T::read_words(&words[T::WORD_COUNT*5 .. T::WORD_COUNT*6])?;
        Ok([val1, val2, val3, val4, val5, val6])
    }
}
pub trait ReadableFromLine {
    type Output;
    fn read_line(line: &str) -> Result<Self::Output, String>;
}
fn split_into_words(line: &str) -> Vec<&str> {
    line.trim_end_matches('\n').split_whitespace().collect()
}
impl<T: Readable> ReadableFromLine for T {
    type Output = T::Output;
    fn read_line(line: &str) -> Result<T::Output, String> {
        let words = split_into_words(line);
        if words.len() != T::WORD_COUNT {
            return Err(format!("line `{}` has {} words, expected {}",
                               line, words.len(), T::WORD_COUNT));
        }
        T::read_words(&words)
    }
}
pub fn read_words_into_vec<T: Readable>(words: &[&str], line: &str) -> Result<Vec<T::Output>, String> {
    let n = T::WORD_COUNT;
    assert_eq!(words.len() % n, 0);
    let mut result = Vec::new();
    for chunk in words.chunks(n) {
        match T::read_words(chunk) {
            Ok(v) => result.push(v),
            Err(msg) => {
                let fragment_msg = if n == 1 {
                    format!("word {}", result.len())
                } else {
                    let l = result.len();
                    format!("words {}-{}", n*l + 1, (n+1) * l)
                };
                return Err(format!(
                    "{} of line `{}`: {}", fragment_msg, line, msg
                ));
            }
        }
    }
    Ok(result)
}
pub fn split_into_words_for_collection<T: Readable>(
    line: &str, prefix_words_count: usize
) -> Result<Vec<&str>, String> {
    let n = T::WORD_COUNT;
    let words = split_into_words(line);
    if words.len() < prefix_words_count {
        return Err(
            format!("line `{}` has {} words, expected at least {}",
                    line, words.len(), prefix_words_count)
        );
    }
    if (words.len() - prefix_words_count) % T::WORD_COUNT != 0 {
        return Err(
            format!("line `{}` has {} words, expected {} + {}",
                    line, words.len(), prefix_words_count, n)
        );
    }
    Ok(words)
}
#[macro_export]
macro_rules! readable_collection {
    ($u:ident => $collection_in:ty, $collection_out:ty) => {
        readable_collection!($u: => $collection_in, $collection_out);
    };
    ($u:ident : $( $bound:path ),* => $collection_in:ty, $collection_out:ty) => {
        impl<$u: Readable> ReadableFromLine for $collection_in
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = $collection_out;
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let words = split_into_words_for_collection::<$u>(line, 0)?;
                Ok(read_words_into_vec::<$u>(&words, line)?.into_iter().collect())
            }
        }
        impl<T1: Readable, $u: Readable> ReadableFromLine for (T1, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = T1::WORD_COUNT;
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let val1 = T1::read_words(&words[..prefix_len])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, $u: Readable> ReadableFromLine for (T1, T2, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2)>::WORD_COUNT;
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::WORD_COUNT;
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::WORD_COUNT;
                let val2 = T2::read_words(&words[start .. start+count2])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, T3: Readable, $u: Readable> ReadableFromLine for (T1, T2, T3, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, T3::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2, T3)>::WORD_COUNT;
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::WORD_COUNT;
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::WORD_COUNT;
                let val2 = T2::read_words(&words[start .. start+count2])?;
                start += count2;
                let count3 = T3::WORD_COUNT;
                let val3 = T3::read_words(&words[start .. start+count3])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, val3, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, $u: Readable> ReadableFromLine for (T1, T2, T3, T4, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, T3::Output, T4::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2, T3, T4)>::WORD_COUNT;
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::WORD_COUNT;
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::WORD_COUNT;
                let val2 = T2::read_words(&words[start .. start+count2])?;
                start += count2;
                let count3 = T3::WORD_COUNT;
                let val3 = T3::read_words(&words[start .. start+count3])?;
                start += count3;
                let count4 = T4::WORD_COUNT;
                let val4 = T4::read_words(&words[start .. start+count4])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, val3, val4, rest.into_iter().collect()))
            }
        }
    };
}
readable_collection!(U => Vec<U>, Vec<U::Output>);
pub fn read<T: ReadableFromLine>() -> T::Output {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    T::read_line(&line).unwrap()
}
#[macro_export]
macro_rules! read {
    () => {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
    };
    ( $pat:pat = $t:ty $(,)* ) => {
        let $pat = read::<$t>();
    };
    ( ! $(,)* ) => {
        let _ = read::<()>();
    };
    ( $pat:pat = $t:ty, $( $rest:tt )+ ) => {
        read_inner!($pat = $t; $($rest)+);
    };
    ( !, $( $rest:tt )+ ) => {
        read_inner!(_ = (); $($rest)+);
    };
}
#[macro_export]
#[doc(hidden)]
macro_rules! read_inner {
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; $pat:pat = $t:ty, $( $rest:tt )* ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , $pat = $t ; $($rest)*);
    };
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; !, $( $rest:tt )* ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , _ = () ; $($rest)*);
    };
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; $pat:pat = $t:ty ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , $pat = $t ;);
    };
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; ! ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , _ = () ;);
    };
    ( $( $pat:pat = $t:ty ),+ ; ) => {
        let ($($pat),+) = read::<($($t),+)>();
    };
}
pub trait ReadableFromChunk {
    type Output;
    fn lines_count() -> usize;
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String>;
}
impl<T1: ReadableFromLine, T2: ReadableFromLine> ReadableFromChunk for (T1, T2) {
    type Output = (T1::Output, T2::Output);
    fn lines_count() -> usize { 2 }
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String> {
        let out1 = T1::read_line(&lines[0])?;
        let out2 = T2::read_line(&lines[1])?;
        Ok((out1, out2))
    }
}
impl<T1: ReadableFromLine, T2: ReadableFromLine, T3: ReadableFromLine> ReadableFromChunk for (T1, T2, T3) {
    type Output = (T1::Output, T2::Output, T3::Output);
    fn lines_count() -> usize { 3 }
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String> {
        let out1 = T1::read_line(&lines[0])?;
        let out2 = T2::read_line(&lines[1])?;
        let out3 = T3::read_line(&lines[2])?;
        Ok((out1, out2, out3))
    }
}
impl<T1: ReadableFromLine, T2: ReadableFromLine, T3: ReadableFromLine, T4: ReadableFromLine> ReadableFromChunk for (T1, T2, T3, T4) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output);
    fn lines_count() -> usize { 4 }
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String> {
        let out1 = T1::read_line(&lines[0])?;
        let out2 = T2::read_line(&lines[1])?;
        let out3 = T3::read_line(&lines[2])?;
        let out4 = T4::read_line(&lines[3])?;
        Ok((out1, out2, out3, out4))
    }
}
pub fn read_chunk<T: ReadableFromChunk>() -> T::Output {
    let stdin = std::io::stdin();
    let mut handle = stdin.lock();
    read_chunk_from_handle::<T>(&mut handle).unwrap()
}
fn read_chunk_from_handle<T: ReadableFromChunk>(handle: &mut std::io::StdinLock) -> Option<T::Output> {
    use std::io::BufRead;
    let mut lines = vec![String::new(); T::lines_count()];
    let mut first = true;
    for line in &mut lines {
        if handle.read_line(line).unwrap() == 0 && first {
            return None;
        }
        first = false;
    }
    Some(T::read_chunk(&lines).unwrap())
}
#[macro_export]
macro_rules! read_chunk {
    ( $( $pat:pat = $t:ty ),+ ) => {
        let ($($pat),+) = read_chunk::<($($t),+)>();
    };
}
static mut STDIN: Option<std::io::Stdin> = None;
pub struct ReadLines<T: ReadableFromLine> {
    lock: std::io::StdinLock<'static>,
    phantom: std::marker::PhantomData<T>
}
impl<T: ReadableFromLine> Iterator for ReadLines<T> {
    type Item = T::Output;
    fn next(&mut self) -> Option<T::Output> {
        use std::io::BufRead;
        let mut line = String::new();
        if self.lock.read_line(&mut line).unwrap() > 0 {
            Some(T::read_line(&line).unwrap())
        } else {
            None
        }
    }
}
pub fn read_lines<T: ReadableFromLine>() -> ReadLines<T> {
    unsafe {
        if STDIN.is_none() {
            STDIN = Some(std::io::stdin());
        }
    }
    ReadLines {
        lock: unsafe { STDIN.as_ref().unwrap().lock() },
        phantom: std::marker::PhantomData::<T>
    }
}
pub struct ReadChunks<T: ReadableFromChunk> {
    lock: std::io::StdinLock<'static>,
    phantom: std::marker::PhantomData<T>
}
impl<T: ReadableFromChunk> Iterator for ReadChunks<T> {
    type Item = T::Output;
    fn next(&mut self) -> Option<T::Output> {
        read_chunk_from_handle::<T>(&mut self.lock)
    }
}
pub fn read_chunks<T: ReadableFromChunk>() -> ReadChunks<T> {
    unsafe {
        if STDIN.is_none() {
            STDIN = Some(std::io::stdin());
        }
    }
    ReadChunks {
        lock: unsafe { STDIN.as_ref().unwrap().lock() },
        phantom: std::marker::PhantomData::<T>
    }
}
pub trait Words {
    fn read<T: Readable>(&self) -> T::Output;
}
impl<'a> Words for [&'a str] {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(self).unwrap()
    }
}
impl<'a> Words for &'a str {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(&[self]).unwrap()
    }
}

// SNIPPET utils
#[macro_export]
macro_rules! echo {
    () => {
        println!()
    };
    ($e: expr $(,)?) => {
        println!("{}", $e)
    };
    ($e: expr, $($es: expr),+ $(,)?) => {
        {
            use std::io::Write;
            let stdout = std::io::stdout();
            let mut handle = stdout.lock();
            write!(handle, "{}", $e).unwrap();
            $(
                write!(handle, " {}", $es).unwrap();
            )+
            writeln!(handle).unwrap();
        }
    };
}
pub fn yn(result: bool) {
    if result {
        println!("Yes");
    } else {
        println!("No");
    }
}
#[allow(non_snake_case)]
pub fn YN(result: bool) {
    if result {
        println!("YES");
    } else {
        println!("NO");
    }
}
pub fn exit(msg: impl std::fmt::Display) -> ! {
    println!("{}", msg);
    std::process::exit(0)
}
#[macro_export]
#[cfg(local)]
macro_rules! dbg {
    () => {
        {
            use std::io::{self, Write};
            writeln!(io::stderr(), "{}: dbg", line!()).unwrap();
        }
    };
    ($e: expr) => {
        {
            use std::io::{self, Write};
            let result = $e;
            writeln!(io::stderr(), "{}: {} = {:?}",
                     line!(), stringify!($e), result)
                .unwrap();
            result
        }
    }
}
#[macro_export]
#[cfg(not(local))]
macro_rules! dbg {
    () => {};
    ($e: expr) => {
        { $e }
    }
}

// END SNIPPETS
// Here is the documentation: https://yoshrc.github.io/rust-atcoder-snippets/atcoder_snippets/index.html

use std::cmp;

fn dfs(i: usize, acc: (usize, i64), ps: &[usize], cs: &[i64], periods: &mut [Option<(usize, i64)>]) -> (usize, i64) {
    if periods[i].is_some() {
        periods[i] = Some(acc);
        acc
    } else {
        periods[i] = Some((0, 0));
        periods[i] = Some(dfs(ps[i], (acc.0 + 1, acc.1 + cs[i]), ps, cs, periods));
        periods[i].unwrap()
    }
}

fn main() {
    read!(n = usize, k = usize);
    read!(ps = Vec<usize_>);
    read!(cs = Vec<i64>);
    let mut periods: Vec<Option<(usize, i64)>> = vec![None; n];
    for i in 0..n {
        if periods[i].is_none() {
            dfs(i, (0, 0), &ps, &cs, &mut periods);
        }
    }
    let periods: Vec<_> = periods.into_iter().map(|x| x.unwrap()).collect();
    let ans: i64 = (0..n).map(|i| {
        let (cycle_len, cycle_sum) = periods[i];
        let (loop_sum, loop_count, rest) = if cycle_sum > 0 {
            let count = (cycle_len / k).saturating_sub(1);
            (cycle_sum * count as i64, count, k - cycle_len*count)
        } else {
            (0, 0, cmp::min(k, cycle_len))
        };
        if loop_count == 0 {
            (1..rest).fold((ps[i], cs[i], cs[i]), |(pos, sum, max), _| {
                (ps[pos], sum + cs[pos], cmp::max(max, sum + cs[pos]))
            }).2
        } else {
            loop_sum + (0..rest).fold((ps[i], cs[i], cs[i]), |(pos, sum, max), _| {
                (ps[pos], sum + cs[pos], cmp::max(max, sum + cs[pos]))
            }).2
        }
    }).max().unwrap();
    echo!(ans);
}