D. Minimum number of steps

{
  "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 ...",
      "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...",
      "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\".  ...",
      "is_translate": false,
      "language": "Formal"
    }
  ]
}