{"problem":{"name":"Xor Sum 4","description":{"content":"We have $N$ integers. The $i$\\-th integer is $A_i$. Find $\\sum_{i=1}^{N-1}\\sum_{j=i+1}^{N} (A_i \\text{ XOR } A_j)$, modulo $(10^9+7)$. What is $\\text{ XOR }$?The XOR of integers $A$ and $B$, $A \\text{","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc147_d"},"statements":[{"statement_type":"Markdown","content":"We have $N$ integers. The $i$\\-th integer is $A_i$.\nFind $\\sum_{i=1}^{N-1}\\sum_{j=i+1}^{N} (A_i \\text{ XOR } A_j)$, modulo $(10^9+7)$.\nWhat is $\\text{ XOR }$?The XOR of integers $A$ and $B$, $A \\text{ XOR } B$, is defined as follows:\n\n*   When $A \\text{ XOR } B$ 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.\n\nFor example, $3 \\text{ XOR } 5 = 6$. (In base two: $011 \\text{ XOR } 101 = 110$.)\n\n## Constraints\n\n*   $2 \\leq N \\leq 3 \\times 10^5$\n*   $0 \\leq A_i < 2^{60}$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $...$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc147_d","tags":[],"sample_group":[["3\n1 2 3","6\n\nWe have $(1\\text{ XOR } 2)+(1\\text{ XOR } 3)+(2\\text{ XOR } 3)=3+2+1=6$."],["10\n3 1 4 1 5 9 2 6 5 3","237"],["10\n3 14 159 2653 58979 323846 2643383 27950288 419716939 9375105820","103715602\n\nPrint the sum modulo $(10^9+7)$."]],"created_at":"2026-03-03 11:01:14"}}