{"problem":{"name":"Xor Sum","description":{"content":"You are given a positive integer $N$. Find the number of the pairs of integers $u$ and $v$ $(0≦u,v≦N)$ such that there exist two non-negative integers $a$ and $b$ satisfying $a$ $xor$ $b=u$ and $a+b=v","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc066_b"},"statements":[{"statement_type":"Markdown","content":"You are given a positive integer $N$. Find the number of the pairs of integers $u$ and $v$ $(0≦u,v≦N)$ such that there exist two non-negative integers $a$ and $b$ satisfying $a$ $xor$ $b=u$ and $a+b=v$. Here, $xor$ denotes the bitwise exclusive OR. Since it can be extremely large, compute the answer modulo $10^9+7$.\n\n## Constraints\n\n*   $1≦N≦10^{18}$\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc066_b","tags":[],"sample_group":[["3","5\n\nThe five possible pairs of $u$ and $v$ are:\n\n*   $u=0,v=0$ (Let $a=0,b=0$, then $0$ $xor$ $0=0$, $0+0=0$.)\n    \n*   $u=0,v=2$ (Let $a=1,b=1$, then $1$ $xor$ $1=0$, $1+1=2$.）\n    \n*   $u=1,v=1$ (Let $a=1,b=0$, then $1$ $xor$ $0=1$, $1+0=1$.）\n    \n*   $u=2,v=2$ (Let $a=2,b=0$, then $2$ $xor$ $0=2$, $2+0=2$.）\n    \n*   $u=3,v=3$ (Let $a=3,b=0$, then $3$ $xor$ $0=3$, $3+0=3$.）"],["1422","52277"],["1000000000000000000","787014179"]],"created_at":"2026-03-03 11:01:14"}}