#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int i = 0; i < (n); ++i)
typedef long long ll;

int N;
vector<ll> a,s;

void dfs(ll p, ll x) {
	if(x != 0)
		s.push_back(x);
	if(p == N)
		return;

	dfs(p+1, x+a.at(p));
	if(x == 0)
		dfs(p+1, 0);
}

int main() {
	ll K,r=0;
	cin >> N >> K;
	a.resize(N);

	rep(i,N)
		cin >> a.at(i);
	dfs(0,0);
	
	rep(i,40) {
		ll t=(1ll<<(39-i))+r, c=0;

		rep(j,s.size())
			if(t == (t&s.at(j)))
				++c;

		if(c >= K)
			r = t;
	}
	
	cout << r << endl;
}
### Prompt

Please formulate a Cpp solution to the following problem:

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.

Examples

Input

4 2
2 5 2 5


Output

12


Input

8 4
9 1 8 2 7 5 6 4


Output

32

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int i = 0; i < (n); ++i)
typedef long long ll;

int N;
vector<ll> a,s;

void dfs(ll p, ll x) {
	if(x != 0)
		s.push_back(x);
	if(p == N)
		return;

	dfs(p+1, x+a.at(p));
	if(x == 0)
		dfs(p+1, 0);
}

int main() {
	ll K,r=0;
	cin >> N >> K;
	a.resize(N);

	rep(i,N)
		cin >> a.at(i);
	dfs(0,0);
	
	rep(i,40) {
		ll t=(1ll<<(39-i))+r, c=0;

		rep(j,s.size())
			if(t == (t&s.at(j)))
				++c;

		if(c >= K)
			r = t;
	}
	
	cout << r << endl;
}
```