大数运算

In this problem you are to calculate the sum of all integers from 1 to n, but you should take all powers of two with minus in the sum.

For example, for n = 4 the sum is equal to  - 1 - 2 + 3 - 4 =  - 4, because 1, 2 and 4 are 20, 21 and 22 respectively.

Calculate the answer for t values of n.

Input

The first line of the input contains a single integer t (1 ≤ t ≤ 100) — the number of values of n to be processed.

Each of next t lines contains a single integer n (1 ≤ n ≤ 109).

Output

Print the requested sum for each of t integers n given in the input.

Examples

Input

2 4 1000000000

Output

-4 499999998352516354

Note

The answer for the first sample is explained in the statement.

计算式： 

代码：

   

import java.math.BigInteger; import java.util.Scanner; public class Main { static final int max=100000000; public static void main(String[] args) { Scanner scan=new Scanner(System.in); int t=scan.nextInt(); while(t!=0){ BigInteger n=scan.nextBigInteger(); BigInteger sum1=n.multiply(n.add(BigInteger.ONE)).divide(BigInteger.valueOf(2)); BigInteger sum2=BigInteger.ZERO; for(int i=0;i<max;i++){ if(BigInteger.valueOf((long) Math.pow(2, i)).compareTo(n)<=0){ continue; } else{ sum2=BigInteger.valueOf(2).multiply(BigInteger.valueOf((long) Math.pow(2, i)).subtract(BigInteger.ONE)); break; } } System.out.println(sum1.subtract(sum2)); t--; } } }