Let's denote as *L*(*x*, *p*) an infinite sequence of integers *y* such that *gcd*(*p*, *y*) = 1 and *y* &gt; *x* (where *gcd* is the greatest common divisor of two integer numbers), sorted in ascending order. The elements of *L*(*x*, *p*) are 1-indexed; for example, 9, 13 and 15 are the first, the second and the third elements of *L*(7, 22), respectively.

You have to process *t* queries. Each query is denoted by three integers *x*, *p* and *k*, and the answer to this query is *k*-th element of *L*(*x*, *p*).
The first line contains one integer *t* (1 ≤ *t* ≤ 30000) — the number of queries to process.

Then *t* lines follow. *i*-th line contains three integers *x*, *p* and *k* for *i*-th query (1 ≤ *x*, *p*, *k* ≤ 10<sup class="upper-index">6</sup>).
none
3
7 22 1
7 22 2
7 22 3
9
13
15
5
42 42 42
43 43 43
44 44 44
45 45 45
46 46 46
187
87
139
128
141
from __future__ import division, print_function
def main():
    prime_factors = [[] for _ in range(10**6 + 1)]
    primes=[True for i in range(10**6+1)]
    def generate_primes(n):
        
        for p in range(2,n+1):
            if primes[p]:
                prime_factors[p].append(p)
                for i in range(2 * p,n+1,p):
                    primes[i] = False
                    prime_factors[i].append(p)
    generate_primes(10**6)
    result = []
    for _ in range(int(input())):
        x, p, k = map(int, input().split())
        arr = prime_factors[p]
        to_add = []
        to_subtract = []
        for i in range(1, 1 << len(arr)):
            mul = 1
            count = 0
            for j in range(len(arr)):
                if (1 << j) & i:
                    count += 1
                    mul *= arr[j]
                
            if count%2:
                to_add.append(mul)
            else:
                to_subtract.append(mul)
        count_before = 0
        for num in to_add:
            count_before += x//num
            
        for num in to_subtract:
            count_before -= x//num
        
        k += (x - count_before)
        
        low = 0
        high = 10**9
        answer = high
        while low <= high:
            mid = (high + low)//2
            temp_count = 0
            for num in to_add:
                temp_count += mid // num
            for num in to_subtract:
                temp_count -= mid // num
            temp_count = mid - temp_count
            if temp_count >= k:
                answer = min(answer, mid)
                high = mid - 1
            else:
                low = mid + 1
        result.append(answer)
    
    print(*result, sep = "\n")

######## Python 2 and 3 footer by Pajenegod and c1729

# Note because cf runs old PyPy3 version which doesn't have the sped up
# unicode strings, PyPy3 strings will many times be slower than pypy2.
# There is a way to get around this by using binary strings in PyPy3
# but its syntax is different which makes it kind of a mess to use.

# So on cf, use PyPy2 for best string performance.

py2 = round(0.5)
if py2:
    from future_builtins import ascii, filter, hex, map, oct, zip
    range = xrange

import os, sys
from io import IOBase, BytesIO

BUFSIZE = 8192
class FastIO(BytesIO):
    newlines = 0

    def __init__(self, file):
        self._file = file
        self._fd = file.fileno()
        self.writable = "x" in file.mode or "w" in file.mode
        self.write = super(FastIO, self).write if self.writable else None

    def _fill(self):
        s = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
        self.seek((self.tell(), self.seek(0,2), super(FastIO, self).write(s))[0])
        return s

    def read(self):
        while self._fill(): pass
        return super(FastIO,self).read()

    def readline(self):
        while self.newlines == 0:
            s = self._fill(); self.newlines = s.count(b"\n") + (not s)
        self.newlines -= 1
        return super(FastIO, self).readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.getvalue())
            self.truncate(0), self.seek(0)

class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        if py2:
            self.write = self.buffer.write
            self.read = self.buffer.read
            self.readline = self.buffer.readline
        else:
            self.write = lambda s:self.buffer.write(s.encode('ascii'))
            self.read = lambda:self.buffer.read().decode('ascii')
            self.readline = lambda:self.buffer.readline().decode('ascii')


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip('\r\n')

# Cout implemented in Python
import sys
class ostream:
    def __lshift__(self,a):
        sys.stdout.write(str(a))
        return self
cout = ostream()
endl = '\n'

# Read all remaining integers in stdin, type is given by optional argument, this is fast
def readnumbers(zero = 0):
    conv = ord if py2 else lambda x:x
    A = []; numb = zero; sign = 1; i = 0; s = sys.stdin.buffer.read()
    try:
        while True:
            if s[i] >= b'0' [0]:
                numb = 10 * numb + conv(s[i]) - 48
            elif s[i] == b'-' [0]: sign = -1
            elif s[i] != b'\r' [0]:
                A.append(sign*numb)
                numb = zero; sign = 1
            i += 1
    except:pass
    if s and s[-1] >= b'0' [0]:
        A.append(sign*numb)
    return A

if __name__== "__main__":
  main()