{"raw_statement":[{"iden":"problem statement","content":"Given are integers $L$ and $R$. Find the number, modulo $10^9 + 7$, of pairs of integers $(x, y)$ $(L \\leq x \\leq y \\leq R)$ such that the remainder when $y$ is divided by $x$ is equal to $y \\text{ XOR } x$.\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: $011 \\text{ XOR } 101 = 110$.)"},{"iden":"constraints","content":"*   $1 \\leq L \\leq R \\leq 10^{18}$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$L$ $R$"},{"iden":"sample input 1","content":"2 3"},{"iden":"sample output 1","content":"3\n\nThree pairs satisfy the condition: $(2, 2)$, $(2, 3)$, and $(3, 3)$."},{"iden":"sample input 2","content":"10 100"},{"iden":"sample output 2","content":"604"},{"iden":"sample input 3","content":"1 1000000000000000000"},{"iden":"sample output 3","content":"68038601\n\nBe sure to compute the number modulo $10^9 + 7$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}