Problem:
Score : 400 points

Problem Statement

We have N integers. The i-th integer is A_i.

Find \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \mbox{ XOR } A_j), modulo (10^9+7).

What is \mbox{ XOR }?

The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:

When A \mbox{ XOR } B is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.

For example, 3 \mbox{ XOR } 5 = 6. (In base two: 011 \mbox{ XOR } 101 = 110.)

Constraints

2 \leq N \leq 3 \times 10^5

0 \leq A_i < 2^{60}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the value \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \mbox{ XOR } A_j), modulo (10^9+7).

Sample Input 1

3
1 2 3

Sample Output 1

6

We have (1\mbox{ XOR } 2)+(1\mbox{ XOR } 3)+(2\mbox{ XOR } 3)=3+2+1=6.

Sample Input 2

10
3 1 4 1 5 9 2 6 5 3

Sample Output 2

237

Sample Input 3

10
3 14 159 2653 58979 323846 2643383 27950288 419716939 9375105820

Sample Output 3

103715602

Print the sum modulo (10^9+7).

Solution in PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

M = 10**9+7
n = int(input())
l = list(map(int,input().split()))
x = max(l)
s = bin(x)
u = len(s)-2
o = [0]*u
for i in l:
    x = bin(i)
    x = x[2:]
    a = list(x)
    d = u - len(a)
    a = (["0"] * d) + a
    j = 0
    while(j < len(o)):
        if a[j] == "1":
            o[j] = o[j]+1

        j = j+1

#print(o)
cnt = 0
z = len(o)*[0]
for i in range(len(o)):
    z[i] = len(l)-o[i]

o = o[::-1]
z = z[::-1]
for r in range(len(l)-1):
    i = l[r]
    x = bin(i)
    x = x[2:]
    a = list(x)
    d = u-len(a)
    a = (["0"]*d)+a
    a = a[::-1]
    j = u - 1
    #print(o,"lo")
    #print(z,"lo")
    while(j > -1):
        if a[j] == "1":
            o[j] = o[j] - 1

        j = j - 1

    j = u-1
    #print(a)
    #print(o)
    while(j > -1):
        if a[j] == "0":
            z[j] = z[j]-1
            cnt = (cnt+((2**j)*o[j])%M)%M

        j = j-1

    j = u-1
    #print(cnt)
    #print(z)
    while (j > -1):
        if a[j] == "1":
            cnt = (cnt + ((2 ** j) * z[j])%M) % M

        j = j - 1

    #print(cnt)

print(cnt)