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 Python (3.8.2) (judge verdict: Accepted)

def readinput():
    n=int(input())
    l=list(map(int,input().split()))
    return n,l

def main(n,a):
    MOD=10**9+7
    hist=[0]*61
    bs=[]
    for i in range(n):
        # s=list(reversed(bin(a[i])[2:]))
        # for j in range(len(s)):
        #     if s[j]=='1':
        #         hist[j]+=1
        # bs.append(s)

        s=bin(a[i])[2:]
        for j in range(len(s)):
            if s[j]=='1':
                hist[len(s)-j-1]+=1
        # j=0
        # ai=a[i]
        # while ai>0:
        #     if ai&1==1:
        #         hist[j]+=1
        #     ai = ai >> 1
        #     j+=1


    #print(bs)
    #print(hist)
    sum=0
    # for i in range(n-1):
    #     s=bs[i]
    #     b=1
    #     for j in range(len(s)):
    #         if s[j]=='0':
    #             sum=(sum+hist[j]*b)%MOD
    #         else:
    #             sum=(sum+( n-i-hist[j] )*b)%MOD
    #             hist[j]-=1
    #         b*=2
    #     for j in range(len(s),61):
    #         sum=(sum+hist[j]*b)%MOD
    #         b*=2
    b=1
    for j in range(61):
        sum=(sum+( hist[j]*(n-hist[j])*b )%MOD )%MOD
        b*=2

    return sum

if __name__=='__main__':
    n,l=readinput()
    ans=main(n,l)
    print(ans)