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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arjundabra:
20141219 06:58:42
do we have to print case no.: for those cases in which no print query is asked???


Divyank Duvedi:
20141203 08:08:19
very nice question.....strict time limits 

Luis Manuel Dï¿½az Barï¿½n:
20141108 09:01:43
Easy and beautiful problem, little bugs leaded me to 7 WAs. Finally AC 

Akhilesh Anandh:
20141104 18:41:38
Weak test cases... Wrote code which considers 1 as a prime number, got Accepted :P


Angel Gonzalez:
20141024 01:35:19
Segment Tree + Sieve + Lazy Propagation = AC :) 

mkrjn99:
20141023 12:55:09
Take care of I/O format.It caused me 1 WA :( 

Aditya Pande:
20141011 10:58:59
getting TLE even with lazy propagation and fast io


Aayush Agarwal:
20140624 22:37:01
After this try this problem :


DEVANSH PARASHAR:
20140512 13:56:12
tle plz any tutorial plz help 

abdou_93:
20131219 16:11:16
finally AC after 9 WA: :) 
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 