codeforces 888 E. Maximum Subsequence（好题）

E. Maximum Subsequence

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given an array a consisting of n integers, and additionally an integer m. You have to choose some sequence of indices b1, b2, ..., bk (1 ≤ b1 < b2 < ... < bk ≤ n) in such a way that the value of  is maximized. Chosen sequence can be empty.

Print the maximum possible value of .

Input

The first line contains two integers n and m (1 ≤ n ≤ 35, 1 ≤ m ≤ 109).

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print the maximum possible value of .

Examples

input

4 45 2 4 1

output

3

input

3 20199 41 299

output

19

Note

In the first example you can choose a sequence b = {1, 2}, so the sum  is equal to 7 (and that's 3 after taking it modulo 4).

In the second example you can choose a sequence b = {3}.

AC code

#include<iostream>#include<vector>#include<algorithm>using namespace std;int n,m;vector<int> A,X,Y;void gen(int l, int r, vector<int> &X){    X.push_back(0);    for (int i=l; i<=r; ++i)    {        int s = X.size();        for (int x=0; x<s; ++x)            X.push_back((A[i]+X[x])%m);    }}int main(){    cin >> n >> m;    A.resize(n);    for (int i=0; i<n; ++i)        cin >> A[i];    int mid = n/2;    gen(0,mid,X);    gen(mid+1,n-1,Y);    sort(Y.begin(),Y.end());    int res = 0;    for (auto ix=X.begin(); ix!=X.end(); ++ix)        res = max(res,*ix + *(upper_bound(Y.begin(),Y.end(),m-1-*ix)-1));    cout << res << endl;    return 0;}