#!/usr/bin/python

import time
import random
import os

def demultiply(product, factor_a_min, factor_a_max, factor_b_min, factor_b_max):
    # Naive solution, brute force.
    
                                                ## x = a * b
                                                ## x in P, P in Z
                                                ## a in Z
                                                ## b in Z
    
    possibilities = []                          ## P
    
    # Loop over all possible values of a.
    factor_a = factor_a_min                     ## a
    while factor_a <= factor_a_max:
        
        if factor_a:
        
            factor_b = product//factor_a        ## b
            # Verify that both a and b are integers.
            if factor_a * factor_b == product:
                
                if factor_b_min <= factor_b <= factor_b_max:
                    possibilities.append((factor_a, factor_b))
        
        factor_a += 1
    
    return possibilities

class tester():
    def __init__(self, factor_a_range, factor_b_range, samples):
        self.factor_a_min, self.factor_a_max = factor_a_range
        self.factor_b_min, self.factor_b_max = factor_b_range
        self.samples = samples
        self.times = []
        self.n_solutions = {}
    
    def one(self):
        a = random.randint(self.factor_a_min, self.factor_a_max)
        b = random.randint(self.factor_b_min, self.factor_b_max)
        
        T0 = time.time()
        P = demultiply(
            a * b,
            self.factor_a_min, self.factor_a_max,
            self.factor_b_min, self.factor_b_max
        )
        T1 = time.time()
        
        self.times.append(T1-T0)
        
        if len(P) in self.n_solutions:
            self.n_solutions[len(P)] += 1
        else:
            self.n_solutions[len(P)] = 1
    
    def test(self):
        self.times = []
        self.n_solutions = {}
        
        for i in range(self.samples):
            self.one()
        
        

def web():
    pass
    

if __name__ == '__main__':
    
    if os.getenv('QUERY_STRING'):
        web()
    
    t = tester((22000000, 23000000), (63000000, 64000000), 1000)