i am getting timeout:

import java.io.; import java.util.; import java.text.; import java.math.; import java.util.regex.*;

public class Solution {

public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    int q = in.nextInt();
    int a;
    int b;
    double abratio;
    int m;
    int perfectpartition;
    int totalpartition;
    double pmratio;
    double discriminant;
    double t;
    double t4;
    double t2;
    for(int i=0;i<q;i++){
        a=in.nextInt();
        b=in.nextInt();
        abratio = (double)a/b;
        m=2;
        totalpartition=0;
        perfectpartition=0;
        for(int k=1;k<=m;k++){
            discriminant = 1+4*k;
            t=Math.log((1+Math.sqrt(discriminant))/2)/Math.log(2);
            t4=Math.round(Math.pow(4,t)*1000000d)/1000000d;
            t2=Math.round(Math.pow(2,t)*1000000d)/1000000d;;
            if(t4==(int)t4 && t2==(int)t2){
                totalpartition++;
                if(Math.round(t*1000000d)/1000000d==(int)t)
                    perfectpartition++;
            }   
            pmratio=(double)perfectpartition/totalpartition;
            if(pmratio<abratio) break;
            else m++;
        }
        System.out.println(m-1);
    }
}

}

Something wrong with my solution. Can't understand what. It does not passed a couple of tests within timeout error:

import math

q = int(input().rstrip())

for _ in range(q): a, b = map(int, input().rstrip().split())

pn = 1 if b/a > 10000: pn = int(math.log(int(b/a),2)) - 1 if pn < 1: pn = 1 start_p2 = 2**pn if pn > 1: start_p2 -=1 start_num_1 = pn

num_1 = start_num_1
cur_p2 = start_p2

k = 2
prev_curp2 = cur_p2  
while 1:
    num_1 += 1
    cur_p2 = 2*cur_p2
    if (num_1-1)*b < a*(cur_p2 - 2):
            k = math.floor(((num_1-1)*b)/a + 2 - cur_p2) + cur_p2
            while (num_1-1)*b < a*(cur_p2 - 2 - k - 1) and (cur_p2 - k - 1 >= prev_curp2):
                k -= 1      
                    break
    prev_curp2 = cur_p2        
k_sum = k**2 - k        
print("{}".format(k_sum))


 prev_curp2 = cur_p2        
k_sum = k**2 - k        
print("{}".format(k_sum))

can anyone explain me why P(15)=2/3 and P(20)=1/2

can anyone explain me how P(15)=2/3 and why P(20)=1/2

Need help to understand the problem. I mean how we are getting P(6) = 1/2?