Di-visible Confusion

题意翻译

### 题目描述 给一个长度为 $n$ 的序列 $a_1,a_2,\dots,a_n$，对于每个位置 $i$，如果 $a_i\%\left(i+1\right)\not=0$，就可以将 $a_i$ 删掉。删掉之后，后面的数都会往前面移动一位。问能否将序列删成空。 ### 输入格式 第一行输入一个正整数 $t$ 表示数据组数。 每组数据输入两行，第一行为一个正整数 $n$ 表示一个序列，第二行 $n$ 个正整数表示序列 $a$。 ### 输出格式 每组数据输出一行，如果能，输出 `YES`，否则输出 `NO`。 ### 数据范围 $1\le t\le10^4,1\le n\le10^5,1\le \sum n\le3\times10^5,1\le a_i\le10^9$。

题目描述

YouKn0wWho has an integer sequence $ a_1, a_2, \ldots, a_n $ . He will perform the following operation until the sequence becomes empty: select an index $ i $ such that $ 1 \le i \le |a| $ and $ a_i $ is not divisible by $ (i + 1) $ , and erase this element from the sequence. Here $ |a| $ is the length of sequence $ a $ at the moment of operation. Note that the sequence $ a $ changes and the next operation is performed on this changed sequence. For example, if $ a=[3,5,4,5] $ , then he can select $ i = 2 $ , because $ a_2 = 5 $ is not divisible by $ i+1 = 3 $ . After this operation the sequence is $ [3,4,5] $ . Help YouKn0wWho determine if it is possible to erase the whole sequence using the aforementioned operation.

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 10\,000 $ ) — the number of test cases. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 10^5 $ ). The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 10^9 $ ). It is guaranteed that the sum of $ n $ over all test cases doesn't exceed $ 3 \cdot 10^5 $ .

输出格式

For each test case, print "YES" (without quotes) if it is possible to erase the whole sequence using the aforementioned operation, print "NO" (without quotes) otherwise. You can print each letter in any register (upper or lower).

输入输出样例

输入样例 #1

5
3
1 2 3
1
2
2
7 7
10
384836991 191890310 576823355 782177068 404011431 818008580 954291757 160449218 155374934 840594328
8
6 69 696 69696 696969 6969696 69696969 696969696

输出样例 #1

YES
NO
YES
YES
NO

说明

In the first test case, YouKn0wWho can perform the following operations (the erased elements are underlined): $ [1, \underline{2}, 3] \rightarrow [\underline{1}, 3] \rightarrow [\underline{3}] \rightarrow [\,]. $ In the second test case, it is impossible to erase the sequence as $ i $ can only be $ 1 $ , and when $ i=1 $ , $ a_1 = 2 $ is divisible by $ i + 1 = 2 $ .