All submissions for this problem are available.### Read problem statements in [Hindi](http://www.codechef.com/download/translated/FEB20/hindi/CASH.pdf), [Bengali](http://www.codechef.com/download/translated/FEB20/bengali/CASH.pdf), [Mandarin Chinese](http://www.codechef.com/download/translated/FEB20/mandarin/CASH.pdf), [Russian](http://www.codechef.com/download/translated/FEB20/russian/CASH.pdf), and [Vietnamese](http://www.codechef.com/download/translated/FEB20/vietnamese/CASH.pdf) as well. Chef wants to take Chefina on a date. However, he has to complete one more task before leaving. Since he does not want to be late, he is asking you for help. There are $N$ bags with coins in a row (numbered $1$ through $N$); for each valid $i$, the $i$-th bag contains $A_i$ coins. Chef should make the number of coins in each bag divisible by a given integer $K$ in the following way: - choose an integer $c$ between $0$ and $N$ (inclusive) - take some coins from the first $c$ bags ― formally, for each $i$ ($1 \le i \le c$), he may choose any number of coins between $0$ and $A_i$ inclusive and take them out of the $i$-th bag - move some of these coins to some of the last $N-c$ bags ― formally, for each $i$ ($c+1 \le i \le N$), he may place a non-negative number of coins in the $i$-th bag Of course, the number of coins placed in the last $N-c$ bags must not exceed the number of coins taken out from the first $c$ bags, but there may be some coins left over. Let's denote the number of these coins by $R$. You should find the smallest possible value of $R$. ### Input - 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 two integers $N$ and $K$. - The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$. ### Output For each test case, print a single line containing one integer ― the smallest value of $R$. ### Constraints - $1 \le T \le 10^3$ - $1 \le N \le 10^5$ - $0 \le A_i \le 10^9$ for each valid $i$ - $1 \le K \le 10^9$ - the sum of $N$ over all test cases does not exceed $10^5$ ### Subtasks **Subtask #1 (10 points):** $K = 2$ **Subtask #2 (20 points):** $N \le 3$ **Subtask #3 (70 points):** original constraints ### Example Input ``` 2 5 7 1 14 4 41 1 3 9 1 10 19 ``` ### Example Output ``` 5 3 ``` ### Explanation **Example case 1:** One of the possible solutions is to choose $c = 4$, remove $1$, $0$, $4$ and $13$ coins from bags $1$, $2$, $3$ and $4$ respectively, and add $13$ coins to bag $5$. **Example case 2:** The optimal solution is to choose $c = 3$ and remove one coin from each bag.
|Tags||cakewalk, feb20, greedy, math, sahi1422, tmwilliamlin|
|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, SQL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, R, COB, FS|
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