Suppose you are performing the following algorithm. There is an array $v_1, v_2, \dots, v_n$ filled with zeroes at start. The following operation is applied to the array several times — at $i$-th step ($0$-indexed) you can:

• either choose position $pos$ ($1 \le pos \le n$) and increase $v_{pos}$ by $k^i$;
• or not choose any position and skip this step.

You can choose how the algorithm would behave on each step and when to stop it. The question is: can you make array $v$ equal to the given array $a$ ($v_j = a_j$ for each $j$) after some step?

Input

The first line contains one integer $T$ ($1 \le T \le 1000$) — the number of test cases. Next $2T$ lines contain test cases — two lines per test case.

The first line of each test case contains two integers $n$ and $k$ ($1 \le n \le 30$, $2 \le k \le 100$) — the size of arrays $v$ and $a$ and value $k$ used in the algorithm.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 10^{16}$) — the array you’d like to achieve.

Output

For each test case print YES (case insensitive) if you can achieve the array $a$ after some step or NO (case insensitive) otherwise.Exampleinput

5
4 100
0 0 0 0
1 2
1
3 4
1 4 1
3 2
0 1 3
3 9
0 59049 810


output

YES
YES
NO
NO
YES


Note

In the first test case, you can stop the algorithm before the $0$-th step, or don’t choose any position several times and stop the algorithm.

In the second test case, you can add $k^0$ to $v_1$ and stop the algorithm.

In the third test case, you can’t make two $1$ in the array $v$.

In the fifth test case, you can skip $9^0$ and $9^1$, then add $9^2$ and $9^3$ to $v_3$, skip $9^4$ and finally, add $9^5$ to $v_2$.

Solution:

 1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950 #include using namespace std; #define rep(i,a,n) for (int i=a;i=a;i--) #define pb push_back #define mp make_pair #define all(x) (x).begin(),(x).end() #define fi first #define se second #define SZ(x) ((int)(x).size()) typedef vector VI; typedef long long ll; typedef pair PII; typedef double db; mt19937 mrand(random_device{}()); const ll mod=1000000007; int rnd(int x) { return mrand() % x;} ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;} ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;} // head   int _,n,k; ll a[1010]; bool check() {     set pos;     rep(i,0,n) {         ll x=a[i];         int d=0;         while (x) {             if (x%k!=0&&x%k!=1) {                 return 0;             }             if (x%k==1) {                 //printf("dd %d\n",d);                 if (pos.count(d)) return 0;                 pos.insert(d);             }             d+=1;             x/=k;         }     }     return 1; } int main() {     for (scanf("%d",&_);_;_--) {         scanf("%d%d",&n,&k);         rep(i,0,n) scanf("%lld",a+i);         puts(check()?"YES":"NO");     } }