A. Bear and Big Brother

Codeforces

IDCF791A

Time1000ms

Memory256MB

Difficulty—

implementation

English · Original

Chinese · Translation

Formal · Original

Bear Limak wants to become the largest of bears, or at least to become larger than his brother Bob. Right now, Limak and Bob weigh _a_ and _b_ respectively. It's guaranteed that Limak's weight is smaller than or equal to his brother's weight. Limak eats a lot and his weight is tripled after every year, while Bob's weight is doubled after every year. After how many full years will Limak become strictly larger (strictly heavier) than Bob? ## Input The only line of the input contains two integers _a_ and _b_ (1 ≤ _a_ ≤ _b_ ≤ 10) — the weight of Limak and the weight of Bob respectively. ## Output Print one integer, denoting the integer number of years after which Limak will become strictly larger than Bob. [samples] ## Note In the first sample, Limak weighs 4 and Bob weighs 7 initially. After one year their weights are 4·3 = 12 and 7·2 = 14 respectively (one weight is tripled while the other one is doubled). Limak isn't larger than Bob yet. After the second year weights are 36 and 28, so the first weight is greater than the second one. Limak became larger than Bob after two years so you should print 2. In the second sample, Limak's and Bob's weights in next years are: 12 and 18, then 36 and 36, and finally 108 and 72 (after three years). The answer is 3. Remember that Limak wants to be larger than Bob and he won't be satisfied with equal weights. In the third sample, Limak becomes larger than Bob after the first year. Their weights will be 3 and 2 then.

熊 Limak 想要成为最大的熊，或者至少比他的兄弟 Bob 重。目前，Limak 和 Bob 的体重分别为 #cf_span[a] 和 #cf_span[b]。保证 Limak 的体重小于或等于他兄弟的体重。 Limak 吃得很多，他的体重每年翻三倍，而 Bob 的体重每年翻倍。经过多少个完整的年后，Limak 的体重会严格大于 Bob？输入仅有一行，包含两个整数 #cf_span[a] 和 #cf_span[b]（#cf_span[1 ≤ a ≤ b ≤ 10]），分别表示 Limak 和 Bob 的体重。请输出一个整数，表示 Limak 的体重严格大于 Bob 所需的年数。在第一个测试用例中，Limak 初始体重为 #cf_span[4]，Bob 初始体重为 #cf_span[7]。一年后，他们的体重分别为 #cf_span[4·3 = 12] 和 #cf_span[7·2 = 14]（一个体重翻三倍，另一个翻倍）。此时 Limak 仍未比 Bob 重。两年后，体重分别为 #cf_span[36] 和 #cf_span[28]，此时第一个体重大于第二个体重。因此 Limak 在两年后变得比 Bob 重，你应该输出 #cf_span[2]。在第二个测试用例中，Limak 和 Bob 未来几年的体重依次为：#cf_span[12] 和 #cf_span[18]，然后是 #cf_span[36] 和 #cf_span[36]，最后是 #cf_span[108] 和 #cf_span[72]（三年后）。答案是 #cf_span[3]。请记住，Limak 希望比 Bob 重，他不会满足于体重相等。在第三个测试用例中，Limak 在第一年后就变得比 Bob 重。那时他们的体重分别为 #cf_span[3] 和 #cf_span[2]。 ## Input 输入仅有一行，包含两个整数 #cf_span[a] 和 #cf_span[b]（#cf_span[1 ≤ a ≤ b ≤ 10]），分别表示 Limak 和 Bob 的体重。 ## Output 请输出一个整数，表示 Limak 的体重严格大于 Bob 所需的年数。 [samples] ## Note 在第一个测试用例中，Limak 初始体重为 #cf_span[4]，Bob 初始体重为 #cf_span[7]。一年后，他们的体重分别为 #cf_span[4·3 = 12] 和 #cf_span[7·2 = 14]（一个体重翻三倍，另一个翻倍）。此时 Limak 仍未比 Bob 重。两年后，体重分别为 #cf_span[36] 和 #cf_span[28]，此时第一个体重大于第二个体重。因此 Limak 在两年后变得比 Bob 重，你应该输出 #cf_span[2]。在第二个测试用例中，Limak 和 Bob 未来几年的体重依次为：#cf_span[12] 和 #cf_span[18]，然后是 #cf_span[36] 和 #cf_span[36]，最后是 #cf_span[108] 和 #cf_span[72]（三年后）。答案是 #cf_span[3]。请记住，Limak 希望比 Bob 重，他不会满足于体重相等。在第三个测试用例中，Limak 在第一年后就变得比 Bob 重。那时他们的体重分别为 #cf_span[3] 和 #cf_span[2]。

**Definitions** Let $ a, b \in \mathbb{Z} $ denote the initial weights of Limak and Bob, respectively, with $ 1 \leq a \leq b \leq 10 $. **Constraints** - $ a \leq b $ **Objective** Find the smallest integer $ y \geq 0 $ such that: $$ a \cdot 3^y > b \cdot 2^y $$

Samples

Input #1

4 7

Output #1

Input #2

4 9

Output #2

Input #3

1 1

Output #3

API Response (JSON)

{
  "problem": {
    "name": "A. Bear and Big Brother",
    "description": {
      "content": "Bear Limak wants to become the largest of bears, or at least to become larger than his brother Bob. Right now, Limak and Bob weigh _a_ and _b_ respectively. It's guaranteed that Limak's weight is sma",
      "description_type": "Markdown"
    },
    "platform": "Codeforces",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "CF791A"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Bear Limak wants to become the largest of bears, or at least to become larger than his brother Bob.\n\nRight now, Limak and Bob weigh _a_ and _b_ respectively. It's guaranteed that Limak's weight is sma...",
      "is_translate": false,
      "language": "English"
    },
    {
      "statement_type": "Markdown",
      "content": "熊 Limak 想要成为最大的熊，或者至少比他的兄弟 Bob 重。\n\n目前，Limak 和 Bob 的体重分别为 #cf_span[a] 和 #cf_span[b]。保证 Limak 的体重小于或等于他兄弟的体重。\n\nLimak 吃得很多，他的体重每年翻三倍，而 Bob 的体重每年翻倍。\n\n经过多少个完整的年后，Limak 的体重会严格大于 Bob？\n\n输入仅有一行，包含两个整数 #cf_span...",
      "is_translate": true,
      "language": "Chinese"
    },
    {
      "statement_type": "Markdown",
      "content": "**Definitions**  \nLet $ a, b \\in \\mathbb{Z} $ denote the initial weights of Limak and Bob, respectively, with $ 1 \\leq a \\leq b \\leq 10 $.\n\n**Constraints**  \n- $ a \\leq b $\n\n**Objective**  \nFind the s...",
      "is_translate": false,
      "language": "Formal"
    }
  ]
}

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