{"raw_statement":[{"iden":"statement","content":"Tavak and Seyyed are good friends. Seyyed is very funny and he told Tavak to solve the following problem instead of _longest-path_.\n\nYou are given _l_ and _r_. For all integers from _l_ to _r_, inclusive, we wrote down all of their integer divisors except 1. Find the integer that we wrote down the maximum number of times.\n\nSolve the problem to show that it's not a _NP_ problem."},{"iden":"input","content":"The first line contains two integers _l_ and _r_ (2 ≤ _l_ ≤ _r_ ≤ 109)."},{"iden":"output","content":"Print single integer, the integer that appears maximum number of times in the divisors.\n\nIf there are multiple answers, print any of them."},{"iden":"examples","content":"Input\n\n19 29\n\nOutput\n\n2\n\nInput\n\n3 6\n\nOutput\n\n3"},{"iden":"note","content":"Definition of a divisor: [https://www.mathsisfun.com/definitions/divisor-of-an-integer-.html](https://www.mathsisfun.com/definitions/divisor-of-an-integer-.html)\n\nThe first example: from 19 to 29 these numbers are divisible by 2: {20, 22, 24, 26, 28}.\n\nThe second example: from 3 to 6 these numbers are divisible by 3: {3, 6}."}],"translated_statement":[{"iden":"statement","content":"Tavak 和 Seyyed 是好朋友。Seyyed 非常有趣，他告诉 Tavak 解决以下问题，而不是 _longest-path_。\n\n给你 #cf_span[l] 和 #cf_span[r]。对于从 #cf_span[l] 到 #cf_span[r]（包含两端）的所有整数，我们写下它们的所有整数因子（除了 #cf_span[1]）。找出我们写下次数最多的那个整数。\n\n解决这个问题，以证明它不是一个 _NP_ 问题。\n\n第一行包含两个整数 #cf_span[l] 和 #cf_span[r]（#cf_span[2 ≤ l ≤ r ≤ 109]）。\n\n输出一个整数，该整数在所有因子中出现次数最多。\n\n如果有多个答案，输出任意一个即可。\n\n因子的定义：https://www.mathsisfun.com/definitions/divisor-of-an-integer-.html\n\n第一个例子：从 #cf_span[19] 到 #cf_span[29]，能被 #cf_span[2] 整除的数是：#cf_span[{20, 22, 24, 26, 28}]。\n\n第二个例子：从 #cf_span[3] 到 #cf_span[6]，能被 #cf_span[3] 整除的数是：#cf_span[{3, 6}]。\n\n"},{"iden":"input","content":"第一行包含两个整数 #cf_span[l] 和 #cf_span[r]（#cf_span[2 ≤ l ≤ r ≤ 109]）。"},{"iden":"output","content":"输出一个整数，该整数在所有因子中出现次数最多。如果有多个答案，输出任意一个即可。"},{"iden":"examples","content":"输入\n19 29\n输出\n2\n输入\n3 6\n输出\n3"},{"iden":"note","content":"因子的定义：https://www.mathsisfun.com/definitions/divisor-of-an-integer-.html\n第一个例子：从 #cf_span[19] 到 #cf_span[29]，能被 #cf_span[2] 整除的数是：#cf_span[{20, 22, 24, 26, 28}]。\n第二个例子：从 #cf_span[3] 到 #cf_span[6]，能被 #cf_span[3] 整除的数是：#cf_span[{3, 6}]。"}],"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ l, r \\in \\mathbb{Z} $ with $ 2 \\leq l \\leq r \\leq 10^9 $.  \nFor each integer $ n \\in [l, r] $, let $ D(n) = \\{ d \\in \\mathbb{Z} \\mid d \\mid n, \\, d > 1 \\} $ be the set of integer divisors of $ n $ excluding 1.  \nLet $ F(d) = \\left| \\left\\{ n \\in [l, r] \\mid d \\in D(n) \\right\\} \\right| $ be the frequency of divisor $ d $ across all $ n \\in [l, r] $.\n\n**Constraints**  \n$ 2 \\leq l \\leq r \\leq 10^9 $\n\n**Objective**  \nFind an integer $ d^* > 1 $ such that:  \n$$\nF(d^*) = \\max_{d > 1} F(d)\n$$  \nIf multiple such $ d^* $ exist, output any one.","simple_statement":null,"has_page_source":false}