{"raw_statement":[{"iden":"problem statement","content":"You are given a positive integer $L$ in base two. How many pairs of non-negative integers $(a, b)$ satisfy the following conditions?\n\n*   $a + b \\leq L$\n*   $a + b = a \\text{ XOR } b$\n\nSince there can be extremely many such pairs, print the count modulo $10^9 + 7$.\n\nWhat is XOR?\n\nThe 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":"*   $L$ is given in base two, without leading zeros.\n*   $1 \\leq L < 2^{100\\ 001}$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$L$"},{"iden":"sample input 1","content":"10"},{"iden":"sample output 1","content":"5\n\nFive pairs $(a, b)$ satisfy the conditions: $(0, 0), (0, 1), (1, 0), (0, 2)$ and $(2, 0)$."},{"iden":"sample input 2","content":"1111111111111111111"},{"iden":"sample output 2","content":"162261460"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}