Chef Restores an Array
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Chef had an array A with length N, but some of its elements got lost. Now, each element of this array is either unknown (denoted by -1) or a positive integer not exceeding K.
Chef decided to restore the array A by replacing each unknown element by a positive integer not exceeding K.
However, Chef has M restrictions that must hold for the restored array. There are two types of restrictions:
- I L R, meaning that for each i such that L < i ≤ R, the condition Ai - Ai-1 = 1 should be satisfied.
- D L R, meaning that for each i such that L < i ≤ R, the condition Ai - Ai-1 = -1 should be satisfied.
Chef would like to know the number of ways to restore the array while satisfying all restrictions, modulo 109+7.
- The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
- The first line of each test case contains three space-separated integers N, M and K.
- The second line contains N integers A1, A2, ..., AN.
- Each of the following M lines contains one restriction in the form I L R or D L R.
For each test case, print a single line containing one integer - the number of ways to restore the array modulo 109+7.
- 1 ≤ T ≤ 10
- 1 ≤ N, M ≤ 100,000
- 1 ≤ K ≤ 1,000,000,000
- 1 ≤ L < R ≤ N
- 1 ≤ Ai ≤ K or Ai = -1 for each valid i
- 1 ≤ sum of N over all test cases ≤ 500,000
- 1 ≤ sum of M over all test cases ≤ 500,000
Input: 3 4 2 10 2 3 5 4 I 1 2 D 3 4 5 2 10 -1 -1 -1 -1 -1 I 1 3 D 3 5 6 2 2 -1 -1 -1 -1 -1 -1 I 1 4 D 4 6 Output: 1 8 0
|Tags||cook92, datastructure, easy-medium, kefaa|
|Time Limit:||1 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.5, 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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