Problem:
Score : 400 points

Problem Statement

One day, Niwango-kun, an employee of Dwango Co., Ltd., found an integer sequence (a_1, ..., a_N) of length N.
He is interested in properties of the sequence a.

For a nonempty contiguous subsequence a_l, ..., a_r (1 \leq l \leq r \leq N) of the sequence a, its beauty is defined as a_l + ... + a_r. Niwango-kun wants to know the maximum possible value of the bitwise AND of the beauties of K nonempty contiguous subsequences among all N(N+1)/2 nonempty contiguous subsequences. (Subsequences may share elements.)

Find the maximum possible value for him.

Constraints

2 \leq N \leq 1000

1 \leq a_i \leq 10^9

1 \leq K \leq N(N+1)/2

All numbers given in input are integers

Input

Input is given from Standard Input in the following format:

N K
a_1 a_2 ... a_N

Output

Print the answer.

Sample Input 1

4 2
2 5 2 5

Sample Output 1

12

There are 10 nonempty contiguous subsequences of a. Let us enumerate them:

contiguous subsequences starting from the first element: \{2\}, \{2, 5\}, \{2, 5, 2\}, \{2, 5, 2, 5\}

contiguous subsequences starting from the second element: \{5\}, \{5, 2\}, \{5, 2, 5\}

contiguous subsequences starting from the third element: \{2\}, \{2, 5\}

contiguous subsequences starting from the fourth element: \{5\}

(Note that even if the elements of subsequences are equal, subsequences that have different starting indices are considered to be different.)

The maximum possible bitwise AND of the beauties of two different contiguous subsequences is 12.
This can be achieved by choosing \{5, 2, 5\} (with beauty 12) and \{2, 5, 2, 5\} (with beauty 14).

Sample Input 2

8 4
9 1 8 2 7 5 6 4

Sample Output 2

32

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"errors"
	"fmt"
	"math"
	"os"
	"sort"
	"strconv"
	"strings"
)

var rdr = bufio.NewReaderSize(os.Stdin, 1000000)

// readLine can read long line string (at least 10^5)
func readLine() string {
	buf := make([]byte, 0, 1000000)
	for {
		l, p, e := rdr.ReadLine()
		if e != nil {
			panic(e)
		}
		buf = append(buf, l...)
		if !p {
			break
		}
	}
	return string(buf)
}

// NextLine reads a line text from stdin, and then returns its string.
func NextLine() string {
	return readLine()
}

/*
var sc = bufio.NewScanner(os.Stdin)

// NextLine reads a line text from stdin, and then returns its string.
func NextLine() string {
	sc.Scan()
	return sc.Text()
}
*/

// NextIntsLine reads a line text, that consists of **ONLY INTEGERS DELIMITED BY SPACES**, from stdin.
// And then returns intergers slice.
func NextIntsLine() []int {
	ints := []int{}
	intsStr := NextLine()
	tmp := strings.Split(intsStr, " ")
	for _, s := range tmp {
		integer, _ := strconv.Atoi(s)
		ints = append(ints, integer)
	}
	return ints
}

// NextStringsLine reads a line text, that consists of **STRINGS DELIMITED BY SPACES**, from stdin.
// And then returns strings slice.
func NextStringsLine() []string {
	str := NextLine()
	return strings.Split(str, " ")
}

// NextRunesLine reads a line text, that consists of **ONLY CHARACTERS ARRANGED CONTINUOUSLY**, from stdin.
// Ant then returns runes slice.
func NextRunesLine() []rune {
	return []rune(NextLine())
}

// Max returns the max integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Max(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m < integer {
			m = integer
		}
	}
	return m
}

// Min returns the min integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Min(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m > integer {
			m = integer
		}
	}
	return m
}

// PowInt is integer version of math.Pow
func PowInt(a, e int) int {
	if a < 0 || e < 0 {
		panic(errors.New("[argument error]: PowInt does not accept negative integers"))
	}
	fa := float64(a)
	fe := float64(e)
	fanswer := math.Pow(fa, fe)
	return int(fanswer)
}

// AbsInt is integer version of math.Abs
func AbsInt(a int) int {
	fa := float64(a)
	fanswer := math.Abs(fa)
	return int(fanswer)
}

// DeleteElement returns a *NEW* slice, that have the same and minimum length and capacity.
// DeleteElement makes a new slice by using easy slice literal.
func DeleteElement(s []int, i int) []int {
	if i < 0 || len(s) <= i {
		panic(errors.New("[index error]"))
	}
	// appendのみの実装
	n := make([]int, 0, len(s)-1)
	n = append(n, s[:i]...)
	n = append(n, s[i+1:]...)
	return n
}

// Concat returns a *NEW* slice, that have the same and minimum length and capacity.
func Concat(s, t []rune) []rune {
	n := make([]rune, 0, len(s)+len(t))
	n = append(n, s...)
	n = append(n, t...)
	return n
}

// UpperRune is rune version of `strings.ToUpper()`.
func UpperRune(r rune) rune {
	str := strings.ToUpper(string(r))
	return []rune(str)[0]
}

// LowerRune is rune version of `strings.ToLower()`.
func LowerRune(r rune) rune {
	str := strings.ToLower(string(r))
	return []rune(str)[0]
}

// ToggleRune returns a upper case if an input is a lower case, v.v.
func ToggleRune(r rune) rune {
	var str string
	if 'a' <= r && r <= 'z' {
		str = strings.ToUpper(string(r))
	} else if 'A' <= r && r <= 'Z' {
		str = strings.ToLower(string(r))
	} else {
		str = string(r)
	}
	return []rune(str)[0]
}

// ToggleString iteratively calls ToggleRune, and returns the toggled string.
func ToggleString(s string) string {
	inputRunes := []rune(s)
	outputRunes := make([]rune, 0, len(inputRunes))
	for _, r := range inputRunes {
		outputRunes = append(outputRunes, ToggleRune(r))
	}
	return string(outputRunes)
}

// Strtoi is a wrapper of `strconv.Atoi()`.
// If `strconv.Atoi()` returns an error, Strtoi calls panic.
func Strtoi(s string) int {
	if i, err := strconv.Atoi(s); err != nil {
		panic(errors.New("[argument error]: Strtoi only accepts integer string"))
	} else {
		return i
	}
}

// sort package (snippets)
//sort.Sort(sort.IntSlice(s))
//sort.Sort(sort.Reverse(sort.IntSlice(s)))
//sort.Sort(sort.Float64Slice(s))
//sort.Sort(sort.StringSlice(s))

// copy function
//a = []int{0, 1, 2}
//b = make([]int, len(a))
//copy(b, a)

/*******************************************************************/

var n, k int
var A []int

func main() {
	tmp := NextIntsLine()
	n, k = tmp[0], tmp[1]
	A = NextIntsLine()

	beauties := make([]int, 500505)

	// 累積和を計算
	sums := [1010]int{}
	sum := 0
	for i := 0; i < n; i++ {
		sum += A[i]
		sums[i] = sum
	}

	// すべての部分列の美しさを計算
	bidx := 0
	for i := 0; i < n; i++ {
		for j := i; j < n; j++ {
			beauty := 0
			if i == j {
				beauty = A[i]
			} else {
				if i == 0 {
					beauty = sums[j]
				} else {
					beauty = sums[j] - sums[i-1]
				}
			}

			beauties[bidx] = beauty
			bidx++
		}
	}

	// beautiesのすべての桁について1の数がk未満の桁をすべて0に置換する
	bitNumbers := [64]int{}
	for _, b := range beauties {
		for i := 0; i < 60; i++ {
			shifted := b >> uint(i)
			bit := shifted & 1
			if bit == 1 {
				bitNumbers[i]++
			}
		}
	}
	for i := 0; i < len(beauties); i++ {
		for j := 0; j < 60; j++ {
			if bitNumbers[j] < k {
				num := beauties[i]
				bit := (num >> uint(j)) & 1
				if bit == 1 {
					beauties[i] -= PowInt(2, j)
				}
			}
		}
	}

	// 降順ソート
	sort.Sort(sort.Reverse(sort.IntSlice(beauties)))

	//	for i := 0; i < n*(n+1)/2; i++ {
	//		fmt.Println(beauties[i])
	//	}

	// 先頭k個の美しさのビット論理積が答え
	ans := beauties[0]
	for i := 1; i < k; i++ {
		ans &= beauties[i]
	}
	fmt.Println(ans)
}