C. Cave Painting

Codeforces

IDCF922C

Time1000ms

Memory256MB

Difficulty—

brute forcenumber theory

English · Original

Chinese · Translation

Formal · Original

Imp is watching a documentary about cave painting. <center>![image](https://espresso.codeforces.com/8ec8a9fff94ac26b2c760e63823e96e9e224b87b.png)</center>Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number _n_ by all integers _i_ from 1 to _k_. Unfortunately, there are too many integers to analyze for Imp. Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all , 1 ≤ _i_ ≤ _k_, are distinct, i. e. there is no such pair (_i_, _j_) that: * 1 ≤ _i_ < _j_ ≤ _k_, * , where is the remainder of division _x_ by _y_. ## Input The only line contains two integers _n_, _k_ (1 ≤ _n_, _k_ ≤ 1018). ## Output Print "_Yes_", if all the remainders are distinct, and "_No_" otherwise. You can print each letter in arbitrary case (lower or upper). [samples] ## Note In the first sample remainders modulo 1 and 4 coincide.

Imp 正在观看一部关于洞穴壁画的纪录片。一些以混乱顺序刻下的数字立即引起了他注意。Imp 快速推测这些数字是某个数 #cf_span[n] 除以从 #cf_span[1] 到 #cf_span[k] 的所有整数 #cf_span[i] 的余数。不幸的是，对于 Imp 来说，要分析的整数太多了。 Imp 希望你检查这些余数是否互不相同。形式化地说，他希望检查所有 #cf_span[1 ≤ i ≤ k] 的余数是否互不相同，即不存在一对 #cf_span[(i, j)] 满足：输入仅包含一行，包含两个整数 #cf_span[n], #cf_span[k] #cf_span[(1 ≤ n, k ≤ 10^{18})]。如果所有余数互不相同，则输出 "_Yes_"，否则输出 "_No_"。你可以以任意大小写形式输出每个字母。在第一个样例中，对 #cf_span[1] 和 #cf_span[4] 取模的余数相同。 ## Input 仅一行包含两个整数 #cf_span[n], #cf_span[k] #cf_span[(1 ≤ n, k ≤ 10^{18})]。 ## Output 如果所有余数互不相同，则输出 "_Yes_"，否则输出 "_No_"。你可以以任意大小写形式输出每个字母。 [samples] ## Note 在第一个样例中，对 #cf_span[1] 和 #cf_span[4] 取模的余数相同。

**Definitions** Let $ n, k \in \mathbb{Z} $ with $ 1 \leq n, k \leq 10^{18} $. Let $ R_i = n \bmod i $ for $ i \in \{1, 2, \dots, k\} $. **Objective** Determine whether all remainders $ R_1, R_2, \dots, R_k $ are distinct.

Samples

Input #1

4 4

Output #1

No

Input #2

5 3

Output #2

Yes

API Response (JSON)

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    "name": "C. Cave Painting",
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      "content": "Imp is watching a documentary about cave painting. <center>![image](https://espresso.codeforces.com/8ec8a9fff94ac26b2c760e63823e96e9e224b87b.png)</center>Some numbers, carved in chaotic order, immedi",
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