Problem:
Score : 500 points

Problem Statement

Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

1 \leq K \leq N \leq 2\times 10^5

|A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N K
A_1 \ldots A_N

Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Sample Input 1

4 2
1 2 -3 -4

Sample Output 1

12

The possible products of the two chosen elements are 2, -3, -4, -6, -8, and 12, so the maximum product is 12.

Sample Input 2

4 3
-1 -2 -3 -4

Sample Output 2

1000000001

The possible products of the three chosen elements are -24, -12, -8, and -6, so the maximum product is -6.

We print this value modulo (10^9+7), that is, 1000000001.

Sample Input 3

2 1
-1 1000000000

Sample Output 3

1000000000

The possible products of the one chosen element are -1 and 1000000000, so the maximum product is 1000000000.

Sample Input 4

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1

Sample Output 4

999983200

Be sure to print the product modulo (10^9+7).

Solution in Rust (1.42.0) (judge verdict: Accepted)

use self::mod_u32::ModU32;
use proconio::input;

fn main() {
    input! {
        n: i64,
        k: i64,
        a: [i64; n],
    };

    let mut na = vec![];
    let mut ma = vec![];
    for &a_i in a.iter() {
        if a_i >= 0 {
            na.push(a_i);
        } else if a_i < 0 {
            ma.push(a_i);
        } else {
            unreachable!()
        }
    }

    let c_n = na.len();
    let c_m = ma.len();
    if if c_n > 0 {
        if n == k {
            c_m % 2 == 0
        } else if n > k {
            true
        } else {
            unreachable!()
        }
    } else {
        k % 2 == 0
    } {
        na.sort_by_key(|&a_i| -a_i.abs());
        ma.sort_by_key(|&a_i| -a_i.abs());

        let mut na2 = vec![];
        for i in (if k % 2 == 0 { 0 } else { 1 }..na.len()).step_by(2) {
            if i + 1 < na.len() {
                na2.push(na[i] * na[i + 1]);
            } else {
                na2.push(na[i]);
            }
        }
        let mut ma2 = vec![];
        for i in (0..ma.len()).step_by(2) {
            if i + 1 < ma.len() {
                ma2.push(ma[i] * ma[i + 1]);
            } else {
                ma2.push(ma[i]);
            }
        }

        let mut i_n = 0_usize;
        let mut i_m = 0_usize;
        let mut ans = if k % 2 == 0 || na.is_empty() {
            ModU32::new(1)
        } else {
            ModU32::new(na[0] as u64)
        };
        while i_n * 2 + i_m * 2 < (k - if k % 2 == 0 { 0 } else { 1 }) as usize {
            let x = match (na2.get(i_n), ma2.get(i_m)) {
                (None, None) => {
                    unreachable!();
                }
                (None, Some(&x)) => {
                    i_m += 1;
                    ModU32::new(x as u64)
                }
                (Some(&x), None) => {
                    i_n += 1;
                    ModU32::new(x as u64)
                }
                (Some(&x), Some(&y)) => {
                    if x >= y {
                        i_n += 1;
                        ModU32::new(x as u64)
                    } else {
                        i_m += 1;
                        ModU32::new(y as u64)
                    }
                }
            };
            ans = ans * x;
        }
        println!("{}", ans);
    } else {
        na.sort_by_key(|&a_i| a_i.abs());
        ma.sort_by_key(|&a_i| a_i.abs());
        let mut i_n = 0;
        let mut i_m = 0;
        let mut ans = ModU32::new(1);
        for _ in 0..k {
            let x = match (na.get(i_n), ma.get(i_m)) {
                (None, None) => unreachable!(),
                (None, Some(&x)) => {
                    i_m += 1;
                    ModU32::new(0) - ModU32::new(x.abs() as u64)
                }
                (Some(&x), None) => {
                    i_n += 1;
                    ModU32::new(x as u64)
                }
                (Some(&x), Some(&y)) => {
                    if x.abs() <= y.abs() {
                        i_n += 1;
                        ModU32::new(x as u64)
                    } else {
                        i_m += 1;
                        ModU32::new(0) - ModU32::new(y.abs() as u64)
                    }
                }
            };
            ans = ans * x;
        }
        println!("{}", ans);
    }
}

mod mod_u32 {
    #[derive(Clone, Copy, Debug, Eq, PartialEq)]
    pub struct ModU32(u32);

    const MODP: u32 = 1_000_000_007;

    impl ModU32 {
        pub fn inv(self) -> Self {
            if self.0 == 0 {
                panic!()
            };
            self.pow(MODP - 2)
        }

        pub fn new(x: u64) -> Self {
            Self((x % (MODP as u64)) as u32)
        }

        pub fn pow(self, exp: u32) -> Self {
            let mut b: ModU32 = self;
            let mut a: ModU32 = Self::new(1);
            let mut x = exp;
            while x > 1 {
                if x & 1 == 1 {
                    a *= b;
                }
                x /= 2;
                b *= b;
            }
            if x == 1 {
                a *= b;
            }
            a
        }
    }

    impl From<u32> for ModU32 {
        fn from(x: u32) -> Self {
            ModU32::new(x as u64)
        }
    }

    impl From<u64> for ModU32 {
        fn from(x: u64) -> Self {
            ModU32::new(x)
        }
    }

    impl From<usize> for ModU32 {
        fn from(x: usize) -> Self {
            ModU32::from(x as u64)
        }
    }

    impl Into<u32> for ModU32 {
        fn into(self) -> u32 {
            self.0
        }
    }

    impl Into<u64> for ModU32 {
        fn into(self) -> u64 {
            self.0 as u64
        }
    }

    impl Into<usize> for ModU32 {
        fn into(self) -> usize {
            self.0 as usize
        }
    }

    impl std::fmt::Display for ModU32 {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }

    impl std::ops::Add<ModU32> for ModU32 {
        type Output = ModU32;

        fn add(self, rhs: ModU32) -> Self::Output {
            (self.0 as u64 + rhs.0 as u64).into()
        }
    }

    impl std::ops::AddAssign<ModU32> for ModU32 {
        fn add_assign(&mut self, rhs: ModU32) {
            self.0 = (*self + rhs).0
        }
    }

    impl std::ops::Sub<ModU32> for ModU32 {
        type Output = ModU32;

        fn sub(self, rhs: ModU32) -> Self::Output {
            (if self.0 < rhs.0 {
                self.0 + (MODP - rhs.0)
            } else {
                self.0 - rhs.0
            })
            .into()
        }
    }

    impl std::ops::SubAssign<ModU32> for ModU32 {
        fn sub_assign(&mut self, rhs: ModU32) {
            self.0 = (*self - rhs).0
        }
    }

    impl std::ops::Mul<ModU32> for ModU32 {
        type Output = ModU32;

        fn mul(self, rhs: ModU32) -> Self::Output {
            Self::new((self.0 as u64) * (rhs.0 as u64))
        }
    }

    impl std::ops::MulAssign<ModU32> for ModU32 {
        fn mul_assign(&mut self, rhs: ModU32) {
            self.0 = (*self * rhs).0
        }
    }

    impl std::ops::Div<ModU32> for ModU32 {
        type Output = ModU32;

        fn div(self, rhs: ModU32) -> Self::Output {
            self * rhs.inv()
        }
    }

    impl std::ops::DivAssign<ModU32> for ModU32 {
        fn div_assign(&mut self, rhs: ModU32) {
            self.0 = (*self / rhs).0
        }
    }
}