{"problem":{"name":"D. Minimum number of steps","description":{"content":"We have a string of letters '_a_' and '_b_'. We want to perform some operations on it. On each step we choose one of substrings \"_ab_\" in the string and replace it with the string \"_bba_\". If we have ","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":1000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF805D"},"statements":[{"statement_type":"Markdown","content":"We have a string of letters '_a_' and '_b_'. We want to perform some operations on it. On each step we choose one of substrings \"_ab_\" in the string and replace it with the string \"_bba_\". If we have no \"_ab_\" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7.\n\nThe string \"_ab_\" appears as a substring if there is a letter '_b_' right after the letter '_a_' somewhere in the string.\n\n## Input\n\nThe first line contains the initial string consisting of letters '_a_' and '_b_' only with length from 1 to 106.\n\n## Output\n\nPrint the minimum number of steps modulo 109 + 7.\n\n[samples]\n\n## Note\n\nThe first example: \"_ab_\"  →  \"_bba_\".\n\nThe second example: \"_aab_\"  →  \"_abba_\"  →  \"_bbaba_\"  →  \"_bbbbaa_\".","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"我们有一个由字母 '_a_' 和 '_b_' 组成的字符串。我们希望对它进行一些操作。在每一步中，我们选择字符串中的一个子串 \"_ab_\"，并将其替换为字符串 \"_bba_\"。当我们不再有任何 \"_ab_\" 子串时，任务完成。请输出使任务完成所需的最少操作步数，结果对 #cf_span[109 + 7] 取模。\n\n字符串 \"_ab_\" 作为子串出现，当且仅当字符串中某处存在字母 '_a_' 后紧跟字母 '_b_'。\n\n第一行包含一个仅由字母 '_a_' 和 '_b_' 组成的初始字符串，长度范围为 #cf_span[1] 到 #cf_span[106]。\n\n请输出最少操作步数，对 #cf_span[109 + 7] 取模。\n\n第一个例子：\"_ab_\" #cf_span[ → ] \"_bba_\"。\n\n第二个例子：\"_aab_\" #cf_span[ → ] \"_abba_\" #cf_span[ → ] \"_bbaba_\" #cf_span[ → ] \"_bbbbaa_\"。\n\n## Input\n\n第一行包含一个仅由字母 '_a_' 和 '_b_' 组成的初始字符串，长度范围为 #cf_span[1] 到 #cf_span[106]。\n\n## Output\n\n请输出最少操作步数，对 #cf_span[109 + 7] 取模。\n\n[samples]\n\n## Note\n\n第一个例子：\"_ab_\" #cf_span[ → ] \"_bba_\"。第二个例子：\"_aab_\" #cf_span[ → ] \"_abba_\" #cf_span[ → ] \"_bbaba_\" #cf_span[ → ] \"_bbbbaa_\"。","is_translate":true,"language":"Chinese"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ s \\in \\{a, b\\}^* $ be the input string of length $ n $, where $ 1 \\leq n \\leq 10^6 $.  \n\n**Operation**  \nIn one step, replace any occurrence of the substring \"ab\" with \"bba\".  \n\n**Goal**  \nCompute the minimum number of such operations until no substring \"ab\" remains, modulo $ 10^9 + 7 $.  \n\n**Objective**  \nLet $ f(s) $ be the minimum number of operations to eliminate all \"ab\" substrings.  \nCompute $ f(s) \\mod (10^9 + 7) $.","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF805D","tags":["combinatorics"],"sample_group":[["ab","1"],["aab","3"]],"created_at":"2026-03-03 11:00:39"}}