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)

pub trait IterScan: Sized {
    type Output;
    fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output>;
}
pub trait MarkedIterScan: Sized {
    type Output;
    fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output>;
}
#[derive(Debug)]
pub struct Scanner<'a> {
    iter: std::str::SplitAsciiWhitespace<'a>,
}
impl<'a> Scanner<'a> {
    #[inline]
    pub fn new(s: &'a str) -> Self {
        let iter = s.split_ascii_whitespace();
        Self { iter }
    }
    #[inline]
    pub fn scan<T: IterScan>(&mut self) -> <T as IterScan>::Output {
        T::scan(&mut self.iter).unwrap()
    }
    #[inline]
    pub fn mscan<T: MarkedIterScan>(&mut self, marker: T) -> <T as MarkedIterScan>::Output {
        marker.mscan(&mut self.iter).unwrap()
    }
    #[inline]
    pub fn scan_vec<T: IterScan>(&mut self, size: usize) -> Vec<<T as IterScan>::Output> {
        (0..size)
            .map(|_| T::scan(&mut self.iter).unwrap())
            .collect()
    }
    #[inline]
    pub fn scan_chars(&mut self) -> Vec<char> {
        self.iter.next().unwrap().chars().collect::<Vec<char>>()
    }
}
mod scanner_impls {
    use super::*;
    macro_rules !iter_scan_impls {($($t :ty ) *) =>{$(impl IterScan for $t {type Output =Self ;#[inline ] fn scan <'a ,I :Iterator <Item =&'a str >>(iter :&mut I ) ->Option <Self >{iter .next () ?.parse ::<$t >() .ok () } } ) *} ;}
    iter_scan_impls !(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String ) ;
    macro_rules !iter_scan_tuple_impl {($($T :ident ) +) =>{impl <$($T :IterScan ) ,+>IterScan for ($($T ,) +) {type Output =($(<$T as IterScan >::Output ,) +) ;#[inline ] fn scan <'a ,It :Iterator <Item =&'a str >>(iter :&mut It ) ->Option <Self ::Output >{Some (($($T ::scan (iter ) ?,) +) ) } } } ;}
    iter_scan_tuple_impl!(A);
    iter_scan_tuple_impl !(A B ) ;
    iter_scan_tuple_impl !(A B C ) ;
    iter_scan_tuple_impl !(A B C D ) ;
    iter_scan_tuple_impl !(A B C D E ) ;
    iter_scan_tuple_impl !(A B C D E F ) ;
    iter_scan_tuple_impl !(A B C D E F G ) ;
    iter_scan_tuple_impl !(A B C D E F G H ) ;
    iter_scan_tuple_impl !(A B C D E F G H I ) ;
    iter_scan_tuple_impl !(A B C D E F G H I J ) ;
    iter_scan_tuple_impl !(A B C D E F G H I J K ) ;
    pub struct ScannerIter<'a, 'b, T> {
        inner: &'b mut Scanner<'a>,
        phantom: std::marker::PhantomData<fn() -> T>,
    }
    impl<'a, 'b, T: IterScan> Iterator for ScannerIter<'a, 'b, T> {
        type Item = <T as IterScan>::Output;
        fn next(&mut self) -> Option<Self::Item> {
            T::scan(&mut self.inner.iter)
        }
    }
    impl<'a> Scanner<'a> {
        #[inline]
        pub fn iter<'b, T: IterScan>(&'b mut self) -> ScannerIter<'a, 'b, T> {
            ScannerIter {
                inner: self,
                phantom: std::marker::PhantomData,
            }
        }
    }
}
mod marker {
    use super::*;
    pub struct Usize1;
    impl IterScan for Usize1 {
        type Output = usize;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            usize::scan(iter).map(|x| x.wrapping_sub(1))
        }
    }
    pub struct Isize1;
    impl IterScan for Isize1 {
        type Output = isize;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            isize::scan(iter).map(|x| x.wrapping_sub(1))
        }
    }
}
#[macro_export]
macro_rules !min {($e :expr ) =>{$e } ;($e :expr ,$($es :expr ) ,+) =>{std ::cmp ::min ($e ,min !($($es ) ,+) ) } ;}
#[macro_export]
macro_rules !chmin {($dst :expr ,$($src :expr ) ,+) =>{{let x =std ::cmp ::min ($dst ,min !($($src ) ,+) ) ;$dst =x ;} } ;}
#[macro_export]
macro_rules !max {($e :expr ) =>{$e } ;($e :expr ,$($es :expr ) ,+) =>{std ::cmp ::max ($e ,max !($($es ) ,+) ) } ;}
#[macro_export]
macro_rules !chmax {($dst :expr ,$($src :expr ) ,+) =>{{let x =std ::cmp ::max ($dst ,max !($($src ) ,+) ) ;$dst =x ;} } ;}
pub trait Modulus: Copy {
    const MODULUS: u32;
    #[inline]
    fn modulo(x: u32) -> u32 {
        x % Self::MODULUS
    }
}
#[allow(unused_macros)]
macro_rules! make_modulus {
    ($t :ident ,$e :expr ) => {
        #[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
        pub struct $t {}
        impl Modulus for $t {
            const MODULUS: u32 = $e;
        }
    };
}
pub mod modulus {
    use super::*;
    #[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
    pub struct Modulo1000000007 {}
    impl Modulus for Modulo1000000007 {
        const MODULUS: u32 = 1_000_000_007;
    }
    #[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
    pub struct Modulo1000000009 {}
    impl Modulus for Modulo1000000009 {
        const MODULUS: u32 = 1_000_000_009;
    }
    #[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
    pub struct Modulo998244353 {}
    impl Modulus for Modulo998244353 {
        const MODULUS: u32 = 998_244_353;
    }
}
#[derive(Copy, Clone, Debug, Default, PartialEq, Eq, Ord, PartialOrd, Hash)]
pub struct MInt<M>
where
    M: Modulus,
{
    x: u32,
    phantom: std::marker::PhantomData<M>,
}
impl<M: Modulus> MInt<M> {
    #[inline]
    pub fn new(x: u32) -> Self {
        Self {
            x: M::modulo(x),
            phantom: std::marker::PhantomData,
        }
    }
    #[inline]
    pub fn new_unchecked(x: u32) -> Self {
        Self {
            x,
            phantom: std::marker::PhantomData,
        }
    }
    #[inline]
    pub fn one() -> Self {
        Self::new_unchecked(1)
    }
    #[inline]
    pub fn zero() -> Self {
        Self::new_unchecked(0)
    }
    #[inline]
    pub fn get_mod() -> u32 {
        M::MODULUS
    }
    #[inline]
    pub fn pow(mut self, mut y: usize) -> Self {
        let mut x = Self::one();
        while y > 0 {
            if y & 1 == 1 {
                x *= self;
            }
            self *= self;
            y >>= 1;
        }
        x
    }
    #[inline]
    pub fn inv(self) -> Self {
        let mut a = self.x;
        let (mut b, mut u, mut s) = (M::MODULUS, 1, 0);
        let k = a.trailing_zeros();
        a >>= k;
        for _ in 0..k {
            if u & 1 == 1 {
                u += M::MODULUS;
            }
            u /= 2;
        }
        while a != b {
            if b < a {
                std::mem::swap(&mut a, &mut b);
                std::mem::swap(&mut u, &mut s);
            }
            b -= a;
            if s < u {
                s += M::MODULUS;
            }
            s -= u;
            let k = b.trailing_zeros();
            b >>= k;
            for _ in 0..k {
                if s & 1 == 1 {
                    s += M::MODULUS;
                }
                s /= 2;
            }
        }
        Self::new_unchecked(s)
    }
}
pub mod modu32_impls {
    use super::*;
    use std::{
        fmt,
        iter::{Product, Sum},
        num::ParseIntError,
        ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
        str::FromStr,
    };
    impl<M: Modulus> From<u32> for MInt<M> {
        #[inline]
        fn from(x: u32) -> Self {
            Self::new(x)
        }
    }
    impl<M: Modulus> From<u64> for MInt<M> {
        #[inline]
        fn from(x: u64) -> Self {
            Self::new_unchecked((x % M::MODULUS as u64) as u32)
        }
    }
    impl<M: Modulus> Add for MInt<M> {
        type Output = Self;
        #[inline]
        fn add(self, rhs: Self) -> Self::Output {
            let mut x = self.x + rhs.x;
            if x >= M::MODULUS {
                x -= M::MODULUS;
            }
            Self::new_unchecked(x)
        }
    }
    impl<M: Modulus> Sub for MInt<M> {
        type Output = Self;
        #[inline]
        fn sub(self, rhs: Self) -> Self::Output {
            if self.x < rhs.x {
                Self::new_unchecked(self.x + M::MODULUS - rhs.x)
            } else {
                Self::new_unchecked(self.x - rhs.x)
            }
        }
    }
    impl<M: Modulus> Mul for MInt<M> {
        type Output = Self;
        #[inline]
        fn mul(self, rhs: Self) -> Self::Output {
            Self::new_unchecked((self.x as u64 * rhs.x as u64 % M::MODULUS as u64) as u32)
        }
    }
    impl<M: Modulus> Div for MInt<M> {
        type Output = Self;
        #[inline]
        fn div(self, rhs: Self) -> Self::Output {
            self * rhs.inv()
        }
    }
    impl<M: Modulus> Neg for MInt<M> {
        type Output = Self;
        #[inline]
        fn neg(self) -> Self::Output {
            if self.x == 0 {
                Self::zero()
            } else {
                Self::new_unchecked(M::MODULUS - self.x)
            }
        }
    }
    impl<M: Modulus> Sum for MInt<M> {
        #[inline]
        fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::zero(), Add::add)
        }
    }
    impl<M: Modulus> Product for MInt<M> {
        #[inline]
        fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::one(), Mul::mul)
        }
    }
    impl<'a, M: Modulus + 'a> Sum<&'a MInt<M>> for MInt<M> {
        #[inline]
        fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::zero(), Add::add)
        }
    }
    impl<'a, M: Modulus + 'a> Product<&'a MInt<M>> for MInt<M> {
        #[inline]
        fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::one(), Mul::mul)
        }
    }
    impl<M: Modulus> fmt::Display for MInt<M> {
        fn fmt<'a>(&self, f: &mut fmt::Formatter<'a>) -> Result<(), fmt::Error> {
            write!(f, "{}", self.x)
        }
    }
    impl<M: Modulus> FromStr for MInt<M> {
        type Err = ParseIntError;
        #[inline]
        fn from_str(s: &str) -> Result<Self, Self::Err> {
            s.parse::<u32>().map(Self::new)
        }
    }
    macro_rules! modu32_ref_binop {
        ($imp :ident ,$method :ident ,$t :ty ) => {
            impl<M: Modulus> $imp<$t> for &$t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: $t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(*self, other)
                }
            }
            impl<M: Modulus> $imp<&$t> for $t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: &$t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(self, *other)
                }
            }
            impl<M: Modulus> $imp<&$t> for &$t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: &$t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(*self, *other)
                }
            }
        };
    }
    modu32_ref_binop!(Add, add, MInt<M>);
    modu32_ref_binop!(Sub, sub, MInt<M>);
    modu32_ref_binop!(Mul, mul, MInt<M>);
    modu32_ref_binop!(Div, div, MInt<M>);
    macro_rules! modu32_ref_unop {
        ($imp :ident ,$method :ident ,$t :ty ) => {
            impl<M: Modulus> $imp for &$t {
                type Output = <$t as $imp>::Output;
                #[inline]
                fn $method(self) -> <$t as $imp>::Output {
                    $imp::$method(*self)
                }
            }
        };
    }
    modu32_ref_unop!(Neg, neg, MInt<M>);
    macro_rules! modu32_ref_op_assign {
        ($imp :ident ,$method :ident ,$t :ty ,$fromimp :ident ,$frommethod :ident ) => {
            impl<M: Modulus> $imp<$t> for $t {
                #[inline]
                fn $method(&mut self, rhs: $t) {
                    *self = $fromimp::$frommethod(*self, rhs);
                }
            }
            impl<M: Modulus> $imp<&$t> for $t {
                #[inline]
                fn $method(&mut self, other: &$t) {
                    $imp::$method(self, *other);
                }
            }
        };
    }
    modu32_ref_op_assign!(AddAssign, add_assign, MInt<M>, Add, add);
    modu32_ref_op_assign!(SubAssign, sub_assign, MInt<M>, Sub, sub);
    modu32_ref_op_assign!(MulAssign, mul_assign, MInt<M>, Mul, mul);
    modu32_ref_op_assign!(DivAssign, div_assign, MInt<M>, Div, div);
}
impl<M: Modulus> IterScan for MInt<M> {
    type Output = Self;
    #[inline]
    fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
        iter.next()?.parse::<MInt<M>>().ok()
    }
}
fn main() {
    #[allow(unused_imports)]
    use std::io::{Read as _, Write as _};
    let __out = std::io::stdout();
    let mut __in_buf = String::new();
    std::io::stdin().read_to_string(&mut __in_buf).unwrap();
    let mut __scanner = Scanner::new(&__in_buf);
    #[allow(unused_macros)]
    macro_rules !scan {() =>{scan !(usize ) } ;(($($t :tt ) ,*) ) =>{($(scan !($t ) ) ,*) } ;([$t :tt ;$len :expr ] ) =>{(0 ..$len ) .map (|_ |scan !($t ) ) .collect ::<Vec <_ >>() } ;({$t :tt =>$f :expr } ) =>{$f (scan !($t ) ) } ;(chars ) =>{__scanner .scan_chars () } ;($t :ty ) =>{__scanner .scan ::<$t >() } ;}
    let mut __out = std::io::BufWriter::new(__out.lock());
    #[allow(unused_macros)]
    macro_rules !print {($($arg :tt ) *) =>(::std ::write !(__out ,$($arg ) *) .unwrap () ) }
    #[allow(unused_macros)]
    macro_rules !println {($($arg :tt ) *) =>(::std ::writeln !(__out ,$($arg ) *) .unwrap () ) }
    #[allow(unused_macros)]
    macro_rules! echo {
        ($iter :expr ) => {
            echo!($iter, "\n")
        };
        ($iter :expr ,$sep :expr ) => {
            let mut iter = $iter;
            if let Some(item) = iter.next() {
                print!("{}", item);
            }
            for item in iter {
                print!("{}{}", $sep, item);
            }
            println!();
        };
    }
    type M = MInt<modulus::Modulo1000000007>;
    let mmm = |x: i64| {
        M::new((((x % M::get_mod() as i64) + M::get_mod() as i64) % M::get_mod() as i64) as u32)
    };
    let n = scan!();
    let k = scan!();
    let mut a = scan!([i64; n]);
    a.sort_by_key(|&x| std::cmp::Reverse(x.abs()));
    let mc = a.iter().take(k).filter(|&&x| x < 0).count();
    let x = a.iter().take(k).map(|&x| mmm(x)).product::<M>();
    if a.iter().take(k).find(|&&x| x == 0).is_some() {
        println!("{}", 0);
    } else if mc % 2 == 0 {
        println!("{}", x);
    } else {
        let mut v = vec![];
        if let Some(&rp) = a.iter().take(k).rev().find(|&&x| x > 0) {
            if let Some(&ln) = a.iter().skip(k).find(|&&x| x < 0) {
                v.push((rp, ln));
            }
        }
        if let Some(&rn) = a.iter().take(k).rev().find(|&&x| x < 0) {
            if let Some(&lp) = a.iter().skip(k).find(|&&x| x > 0) {
                v.push((rn, lp));
            }
        }
        let x = match v.len() {
            0 => a.iter().rev().take(k).map(|&x| mmm(x)).product::<M>(),
            1 => {
                if v[0].0 == 0 {
                    return;
                }
                x / mmm(v[0].0) * mmm(v[0].1)
            }
            2 => {
                let (l1, r1) = v[0];
                let (l2, r2) = v[1];
                if l1 == 0 || l2 == 0 {
                    return;
                }
                if r1.abs() * l2.abs() > l1.abs() * r2.abs() {
                    x / mmm(l1) * mmm(r1)
                } else {
                    x / mmm(l2) * mmm(r2)
                }
            }
            _ => return,
        };
        println!("{}", x);
    }
}