Integral Array

문제

You are given an array $aa$ of $nn$ positive integers numbered from $11$ to $nn$. Let's call an array integral if for any two, not necessarily different, numbers $xx$ and $yy$ from this array, $x\ge yx\; \backslash ge\; y$, the number $\lfloor \frac{x}{y}\rfloor \backslash left\; \backslash lfloor\; \backslash frac\{x\}\{y\}\; \backslash right\; \backslash rfloor$ ($xx$ divided by $yy$ with rounding down) is also in this array.

You are guaranteed that all numbers in $aa$ do not exceed $cc$. Your task is to check whether this array is integral.

입력

The input consists of multiple test cases. The first line contains a single integer $tt$ ($1\le t\le 100001\; \backslash le\; t\; \backslash le\; 10\backslash ,000$) --- the number of test cases. Description of the test cases follows.

The first line of each test case contains two integers $nn$ and $cc$ ($1\le n\le {10}^{6}1\; \backslash le\; n\; \backslash le\; 10^6$, $1\le c\le {10}^{7}1\; \backslash le\; c\; \backslash le\; 10^7$) --- the size of $aa$ and the limit for the numbers in the array.

The second line of each test case contains $nn$ integers $a_{1}a\_1$, $a_{2}a\_2$, $\dots \backslash ldots$, $a_{n}a\_n$ ($1\le a_i\le c1\; \backslash le\; a\_i\; \backslash le\; c$) --- the array $aa$.

Let $NN$ be the sum of $nn$ over all test cases and $CC$ be the sum of $cc$ over all test cases. It is guaranteed that $N\le {10}^{6}N\; \backslash le\; 10^6$ and $C\le {10}^{7}C\; \backslash le\; 10^7$.

출력

For each test case print Yes if the array is integral and No otherwise.

힌트

In the first test case it is easy to see that the array is integral:

• $\lfloor \frac{1}{1}\rfloor =1\backslash left\; \backslash lfloor\; \backslash frac\{1\}\{1\}\; \backslash right\; \backslash rfloor\; =\; 1$, $a_1=1a\_1\; =\; 1$, this number occurs in the arry
• $\lfloor \frac{2}{2}\rfloor =1\backslash left\; \backslash lfloor\; \backslash frac\{2\}\{2\}\; \backslash right\; \backslash rfloor\; =\; 1$
• $\lfloor \frac{5}{5}\rfloor =1\backslash left\; \backslash lfloor\; \backslash frac\{5\}\{5\}\; \backslash right\; \backslash rfloor\; =\; 1$
• $\lfloor \frac{2}{1}\rfloor =2\backslash left\; \backslash lfloor\; \backslash frac\{2\}\{1\}\; \backslash right\; \backslash rfloor\; =\; 2$, $a_2=2a\_2\; =\; 2$, this number occurs in the array
• $\lfloor \frac{5}{1}\rfloor =5\backslash left\; \backslash lfloor\; \backslash frac\{5\}\{1\}\; \backslash right\; \backslash rfloor\; =\; 5$, $a_3=5a\_3\; =\; 5$, this number occurs in the array
• $\lfloor \frac{5}{2}\rfloor =2\backslash left\; \backslash lfloor\; \backslash frac\{5\}\{2\}\; \backslash right\; \backslash rfloor\; =\; 2$, $a_2=2a\_2\; =\; 2$, this number occurs in the array

Thus, the condition is met and the array is integral.

In the second test case it is enough to see that

$\lfloor \frac{7}{3}\rfloor =\lfloor 2\frac{1}{3}\rfloor =2\backslash left\; \backslash lfloor\; \backslash frac\{7\}\{3\}\; \backslash right\; \backslash rfloor\; =\; \backslash left\; \backslash lfloor\; 2\backslash frac\{1\}\{3\}\; \backslash right\; \backslash rfloor\; =\; 2$, this number is not in $aa$, that's why it is not integral.

In the third test case $\lfloor \frac{2}{2}\rfloor =1\backslash left\; \backslash lfloor\; \backslash frac\{2\}\{2\}\; \backslash right\; \backslash rfloor\; =\; 1$, but there is only $22$ in the array, that's why it is not integral.

3
3 5
1 2 5
4 10
1 3 3 7
1 2
2

Yes
No
No