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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace Practice
{
	class Program
	{
		static void Main(string[] args)
		{
			Solve();
		}
		private const int MOD = 10007;// 1000000007;
		static void Solve()
		{
			var o = ReadAndParseIntArr();
			var n = o[0];
			var k = o[1];
			var a = ReadAndParseLongArr();
			var sumA = new long[n + 1];
			for(int i=0;i<n;++i)
			{
				sumA[i + 1] = sumA[i] + a[i];
			}

			var b = new long[n * (n + 1) / 2];
			int idx = 0;
			for(int total = 1;total<=n;++total)
			{
				for(int i=0;i+total<sumA.Length;++i)
				{
					b[idx++] = sumA[i + total] - sumA[i];
				}
			}

			var listB = new List<long>(b);
			listB.Sort();
			listB.Reverse();
			long ans = listB[0];
			for(int i=1;i<k;++i)
			{
				ans &= listB[i];
			}
			Console.WriteLine(ans);
		}
		


		#region よく使う便利関数a
		private static bool isPrime(long x)
		{
			if(x == 2) { return true; }
			if(x < 2 || x % 2 == 0) { return false; }
			long i = 3;
			while(i * i <= x)
			{
				if(x % i == 0) { return false; }
				i = i + 2;
			}
			return true;
		}
		private static long lcm(long x, long y)
		{
			return x / gcd(x, y) * y;
		}
		private static long gcd(long x, long y)
		{
			return y > 0 ? gcd(y, x % y) : x;
		}
		private static long pow(long x, long n)
		{
			if(n == 0) { return 1; }
			long res = pow(x * x % MOD, n / 2);
			if(n % 2 == 1)
			{
				res = res * x % MOD;
			}
			return res;
		}
		private static int ReadAndParseInt()
		{
			return int.Parse(Console.ReadLine());
		}
		private static int[] ReadAndParseIntArr()
		{
			return Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
		}
		private static long ReadAndParseLong()
		{
			return long.Parse(Console.ReadLine());
		}
		private static long[] ReadAndParseLongArr()
		{
			return Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
		}

		/// <summary>
		/// 指定した値以上の先頭のインデクスを返す
		/// </summary>
		/// <typeparam name="T">比較する値の型</typeparam>
		/// <param name="arr">対象の配列（※ソート済みであること）</param>
		/// <param name="start">開始インデクス [inclusive]</param>
		/// <param name="end">終了インデクス [exclusive]</param>
		/// <param name="value">検索する値</param>
		/// <param name="comparer">比較関数(インターフェイス)</param>
		/// <returns>指定した値以上の先頭のインデクス</returns>
		public static int LowerBound<T>(IReadOnlyList<T> arr, int start, int end, T value, IComparer<T> comparer)
		{
			int low = start;
			int high = end;
			int mid;
			while(low < high)
			{
				mid = ((high - low) >> 1) + low;
				if(comparer.Compare(arr[mid], value) < 0)
					low = mid + 1;
				else
					high = mid;
			}
			return low;
		}

		//引数省略のオーバーロード
		public static int LowerBound<T>(IReadOnlyList<T> arr, T value) where T : IComparable
		{
			return LowerBound(arr, 0, arr.Count, value, Comparer<T>.Default);
		}

		/// <summary>
		/// 指定した値より大きい先頭のインデクスを返す
		/// </summary>
		/// <typeparam name="T">比較する値の型</typeparam>
		/// <param name="arr">対象の配列（※ソート済みであること）</param>
		/// <param name="start">開始インデクス [inclusive]</param>
		/// <param name="end">終了インデクス [exclusive]</param>
		/// <param name="value">検索する値</param>
		/// <param name="comparer">比較関数(インターフェイス)</param>
		/// <returns>指定した値より大きい先頭のインデクス</returns>
		public static int UpperBound<T>(IReadOnlyList<T> arr, int start, int end, T value, IComparer<T> comparer)
		{
			int low = start;
			int high = end;
			int mid;
			while(low < high)
			{
				mid = ((high - low) >> 1) + low;
				if(comparer.Compare(arr[mid], value) <= 0)
					low = mid + 1;
				else
					high = mid;
			}
			return low;
		}

		//引数省略のオーバーロード
		public static int UpperBound<T>(IReadOnlyList<T> arr, T value)
		{
			return UpperBound(arr, 0, arr.Count, value, Comparer<T>.Default);
		}
		#endregion
	}
}