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# Find an index in an array such that its prefix sum equals its suffix sum.

A zero-indexed array A consisting of N integers is given. An equilibrium index of this array is any integer P such that 0 ≤ P < N and the sum of elements of lower indices is equal to the sum of elements of higher indices, i.e.
A + A + ... + A[P−1] = A[P+1] + ... + A[N−2] + A[N−1].
Sum of zero elements is assumed to be equal to 0. This can happen if P = 0 or if P = N−1.
For example, consider the following array A consisting of N = 8 elements:
A = -1 A = 3 A = -4 A = 5 A = 1 A = -6 A = 2 A = 1
P = 1 is an equilibrium index of this array, because:
• A = −1 = A + A + A + A + A + A
P = 3 is an equilibrium index of this array, because:
• A + A + A = −2 = A + A + A + A
P = 7 is also an equilibrium index, because:
• A + A + A + A + A + A + A = 0
and there are no elements with indices greater than 7.
P = 8 is not an equilibrium index, because it does not fulfill the condition 0 ≤ P < N.
Write a function:
class Solution { public int solution(int[] A); }
that, given a zero-indexed array A consisting of N integers, returns any of its equilibrium indices. The function should return −1 if no equilibrium index exists.
For example, given array A shown above, the function may return 1, 3 or 7, as explained above.
Assume that:
• N is an integer within the range [0..100,000];
• each element of array A is an integer within the range [−2,147,483,648..2,147,483,647].
Complexity:
• expected worst-case time complexity is O(N);
• expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments).
Elements of input arrays can be modified.

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Solution:

`import java.math.BigInteger;public class Solution {    private static BigInteger sub = BigInteger.ZERO;    private static BigInteger sum = BigInteger.ZERO;    private static BigInteger left = BigInteger.ZERO;    private static BigInteger right = BigInteger.ZERO;    public static void main(String[] args) throws Exception {        Solution s = new Solution();        int[] A = {-1, 3, -4, 5, 1, -6, 2, 1};        System.out.print(s.solution(A));    }    public int solution(int[] A) {        sum = BigInteger.ZERO;        if (A.length != -1 ) {            sum = sum.add(sumOfSubArray(A));        }        for (int i=0; i<A.length; i++) {            sub = sub.add(BigInteger.valueOf(A[i]));            left = sub.subtract(BigInteger.valueOf(A[i]));            right = sum.subtract(sub);            if ( left.equals(right)) {                return i;            }        }        return -1;    }    public static BigInteger sumOfSubArray(int[] a) {        BigInteger sum = BigInteger.ZERO;        for (int i = 0; i < a.length; i++) {            sum = sum.add(BigInteger.valueOf(a[i]));        }        return sum;    }}` 