Chef and Gcd Queries
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Chef likes solving problems involving a lot of queries with numbers. One day, he found a new problem which he finds difficult to solve. Therefore, he's asking for your help!
You are given a sequence A1, A2, ..., AN and Q queries. There are two types of queries:
- 1 X Y — Set AX = Y.
- 2 L R G — Compute the number of indices i such that L ≤ i ≤ R and gcd(G, Ai) = 1.
Find the answer to each query of the second type.
Note: gcd(X, Y) denotes the greatest common divisor — the highest positive integer which divides both X and Y.
- The first line of the input contains a single integer N denoting the number of elements in the sequence.
- The second line contains N space-separated integers A1, A2, ..., AN.
- The third line contains a single integer Q denoting the number of queries.
- Each of the following Q lines describes one query in the following format:
- 1 X Y for a query of the first type
- 2 L R G for a query of the second type
For each query of type 2, print a single line containing one integer - the answer to the query.
- 1 ≤ N, Q ≤ 5 · 104
- 1 ≤ L ≤ R ≤ N
- 1 ≤ X ≤ N
- 1 ≤ Y, G ≤ 105
- 1 ≤ Ai ≤ 105 for each valid i
Subtask #1 (15 points): 1 ≤ N, Q ≤ 1000
Subtask #2 (85 points): original constraints
Input: 4 2 3 4 5 3 2 1 4 2 1 2 6 2 1 4 2 Output: 2 1
In the first query, gcd(A2, 2) = 1 and gcd(A4, 2) = 1, so the answer is 2.
In the third query, only gcd(A4, 2) is equal to 1, so the answer is 1.
|Tags||inclusion-exclusion, march18, medium, mobius, vipsharmavip|
|Time Limit:||1 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, CLOJ, COB, FS|
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