Having difficulty in understanding the logic of balanced partitioning

I was solving a problem of balanced partitioning from this link. In this question we have to divide the array in equal parts such that the difference between their sum is least. So, the solution I found out is considering all the cases whether a element will be included in one group or not means we have to try all 2^n cases.

I came up with a solution who divided the array using bit manipulation and I am not getting the logic. I am posting the code below. Someone please tell me how is he dividing the array?

#include<bits/stdc++.h>
using namespace std;
#define N 11

void solve(int a[N])
{
    long long x,y,v1,v2,res,i,j;
    long long val=1<<N;
    res=INT_MAX;
    for(i=0;i<val;i++)
    {
        x=y=v1=v2=0;
        for(j=0;j<N;j++)
        {
            if(i & (1<<j))
            {
                x++;
                v1+=a[j];
            }
            else
            {
                y++;
                v2+=a[j];
            }
        }
        if(abs(x-y)<=1) res=min(res,abs(v1-v2));
    }
    cout<<res<<endl;
}
int main()
{
    int a[] = {23, 45, -34, 12, 0, 98, -99, 4, 189, -1, 4};
    solve(a);
    return 0;
}