CNTPRIME  Counting Primes
Tortoise and Achilles are playing the Counting the Primes game. Achilles will give Tortoise some numbers, and some intervals, and then Tortoise needs to count the primes on those intervals. It is an easy game, but Tortoise is doing the counting slowly. Achilles is pissed off, so he has given you the task as you are a good programmer. For a twist, he has changed the game a little bit, that is he will give some intervals for counting the prime as well as he will give some intervals to change the numbers in that interval.
You are given an array of n elements. After that you will be given M commands. They are 
 0 x y v  you have to change all numbers in the range of x to y (inclusive) to v, where x and y are two indexes of the array.
 1 x y  output a line containing a single integer which is the number of primes between x and y (inclusive).
The array is indexed from 1 to n.
Input:
Input starts with an integer T (≤ 10), denoting the number of test cases.
Each case contains two integers n (1 ≤ n ≤ 10^{4}) and q (1 ≤ q ≤ 2*10^{4}). Then next line, you will be given N integers. After that each of the next q lines will contain a task in one of the following form:
 0 x y v (1 ≤ x ≤ y ≤ n, 2 ≤ v ≤ 10^{6})
 1 x y (1 ≤ x ≤ y ≤ n)
And the numbers will be in range of [2, 10^{6}].
Output:
For each case, print the case number first. Then for each query '1 x y', print the number of primes between x and y [inclusively].
Sample Input 
Output for Sample Input 
1 5 3 78 2 13 12 3 1 1 2 0 4 4 5 1 1 5 
Case 1: 1 4 
Note:
 Use Faster IO like scanf,printf
 A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first prime numbers are 2,3,5,7,11....2,3,5,7,11,…
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(Tjandra Satria Gunawan)(æ›¾æ¯…æ˜†):
20131219 16:11:16
Haha, finally AC after 5 WA... It's hard to debug huge code, but seems that my complex bitwise data structure become the FASTEST algo I ever created :D 

Ehor Nechiporenko:
20131219 16:11:16
Really nice problem. It contains quite good ways to optimize! 

Faiyaz:
20131219 16:11:16
@DEVANSH PARASHAR , mayb more fast solution exists.. :) Last edit: 20121217 06:35:54 

DEVANSH PARASHAR:
20131219 16:11:16
time too less for this plz increase time i have used the fastest methods to solve this problem then too i get tle 
Added by:  Faiyaz 
Date:  20121216 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Own Problem 