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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sriankit:
20131219 16:11:16
Lazy propagation gives TLE in java.. :( 

(Tjandra Satria Gunawan)(æ›¾æ¯…æ˜†):
20131219 16:11:16
@akb: I didn't use segment tree to solve this problem, so I don't know. But, I know that the constraints is correct (no case with n>10^4). 

akb:
20131219 16:11:16
someone please explain me why segtree size 6*10^4 is giving WA but 10^5 is AC.


mehmetin:
20131219 16:11:16
Lazy Prop. with optimized IO passes Last edit: 20121223 22:59:23 

(Tjandra Satria Gunawan)(æ›¾æ¯…æ˜†):
20131219 16:11:16
@Mehmet Inal: You need an efficient data structure to solve this problem. 

mehmetin:
20131219 16:11:16
Should we use lazy propagation? Last edit: 20121223 13:26:44 

npsabari:
20131219 16:11:16
Segment Tree with 3*10^4 nodes gave WA. but with 4*10^4 nodes gave AC. But as n <= 10^4 the first one should have got AC.. So be careful while choosing the array sizes 

Rahul Shah:
20131219 16:11:16
can anyone provide some tricky test cases...my code is giving right for almost all inputs.. Last edit: 20121221 10:55:24 

Aditya Pande:
20131219 16:11:16
got TLE with my first attempt


(Tjandra Satria Gunawan)(æ›¾æ¯…æ˜†):
20131219 16:11:16
ok, done... 2.2M of memory and 0.3s time... this is my best :D 
Added by:  Faiyaz 
Date:  20121216 
Time limit:  0.234s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Own Problem 