Problem: There is an infinite set generated as follows:

  * 1 is in this set. 
  * If x is in this set, x ⋅ a and x+b both are in this set. 



For example, when a=3 and b=6, the five smallest elements of the set are:

  * 1, 
  * 3 (1 is in this set, so 1⋅ a=3 is in this set), 
  * 7 (1 is in this set, so 1+b=7 is in this set), 
  * 9 (3 is in this set, so 3⋅ a=9 is in this set), 
  * 13 (7 is in this set, so 7+b=13 is in this set). 



Given positive integers a, b, n, determine if n is in this set.

Input

The input consists of multiple test cases. The first line contains an integer t (1≤ t≤ 10^5) — the number of test cases. The description of the test cases follows.

The only line describing each test case contains three integers n, a, b (1≤ n,a,b≤ 10^9) separated by a single space.

Output

For each test case, print "Yes" if n is in this set, and "No" otherwise. You can print each letter in any case.

Example

Input


5
24 3 5
10 3 6
2345 1 4
19260817 394 485
19260817 233 264


Output


Yes
No
Yes
No
Yes

Note

In the first test case, 24 is generated as follows:

  * 1 is in this set, so 3 and 6 are in this set; 
  * 3 is in this set, so 9 and 8 are in this set; 
  * 8 is in this set, so 24 and 13 are in this set. 



Thus we can see 24 is in this set.

The five smallest elements of the set in the second test case is described in statements. We can see that 10 isn't among them.

Solution (in PYTHON3):

Solution:
#ANKIT BEHIND THE KEYBOARD
"""To increase the size of recursion stack in python
    *************************************************
import resource, sys
resource.setrlimit(resource.RLIMIT_STACK, (2**29,-1))
sys.setrecursionlimit(10**6)"""


"""#segment tree
BUILD
def segmenttree(tree,A,node,start,end):
    if(start==end):
        tree[node]=A[start]
    else:
        mid=(start+end)//2
        segmenttree(2*node,start,mid)
        segmenttree(2*node+1,mid+1,end)
        tree[node]=tree[2*node+1]+tree[2*node+2]
################################################
To query on a given range, check 3 conditions.
   **********************************************
Range represented by a node is completely inside the given range
Range represented by a node is completely outside the given range
Range represented by a node is partially inside and partially outside the given range

for sum of query in l,r ####tree is represented in array
********************************************************
Input array
*********
A=[]
find pow of two just greater than the len of input array ex:N=3 then l=2*4-1
tree=[0]*l
max length of segtree will be 4N so u can say l=4*N worst case
def query(tree,A,node,start,end,l,r):
    if(r<start or l>end):
        return 0
    if(l<=start and r>=end):
        return tree[node]
    mid=(start+end)//2
    p1=query(tree,A,2*node+1,start,mid,l,r)
    p2=query(tree,A,2*node+2,mid+1,end,l,r)
    return p1+p2
O(4*logN)
#Update a value in segment tree
*******************************
1)Start with root of segment tree.
2) If array index to be updated is not in current node’s range, then return
3) Else update current node and recur for children.
def update(tree,A,node,start,end,idx,val):
    if(start==end):
        A[idx]+=val
        tree[node]+=val
    else:
        mid=(start+end)//2
        if(start<=idx and idx<=mid):
            update(tree,A,2 * node+1, start, mid, idx, val)
        else:
            update(tree,A,2 * node + +2, mid + 1, end, idx, val)
        tree[node] = tree[2 * node+1] + tree[2 * node + 2]

O(logN)"""
t=int(input())
for i in range(0,t):
    n,a,b=map(int,input().split())
    if(a==1):
        if((n-1)%b==0):
            print("Yes")
        else:
            print("No")
    else:
        ans=0
        r=1
        while(r<=n):
            if((n-r)%b==0):


                ans=1
                break
            r=r*a
        if(ans==1):
            print("Yes")
        else:
            print("No")