{"problem":{"name":"Sum Equals Xor","description":{"content":"You are given a positive integer $L$ in base two. How many pairs of non-negative integers $(a, b)$ satisfy the following conditions? *   $a + b \\leq L$ *   $a + b = a \\text{ XOR } b$ Since there can","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc129_e"},"statements":[{"statement_type":"Markdown","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: $011 \\text{ XOR } 101 = 110$.)\n\n## Constraints\n\n*   $L$ is given in base two, without leading zeros.\n*   $1 \\leq L < 2^{100\\ 001}$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$L$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc129_e","tags":[],"sample_group":[["10","5\n\nFive pairs $(a, b)$ satisfy the conditions: $(0, 0), (0, 1), (1, 0), (0, 2)$ and $(2, 0)$."],["1111111111111111111","162261460"]],"created_at":"2026-03-03 11:01:14"}}