Chefs new Pet

Problem code: HAREJUMP

All submissions for this problem are available.

The chef got a new rabbit and he is going to train him so that he can perform for him whenever he needs entertainment. The chef teaches k types of jumps to the rabbit. Each jump has definite length L units. The rabbit does not have any brains he will use any type of jump he feels like at any point of time. He is placed on a very long mat and starts at 0 unit. The chef wants to know in how many ways he can perform his jumps and cover exactly N units of distance.

Input

The first line contains the number of the test cases T(<=100). Each test case consists of 2 lines. The first line defines the distance N (1<=N<=10^18) which tells us the number of units the chef wants the rabbit to cover. The next line contains k the number of jumps which are taught to the rabbit, k (k<=15) integers follow in the same line each denoting distinct distance L (L<=15) units which can be jumped by the rabbit.

Output

Print T integers each denoting the number of ways the rabbit can perform jumps of N units of distance. Print the remainder obtained on dividing the answer by 1000000007 if the answer is greater than or equal to 1000000007.

Example

Input:
3
10
1 1
13
3 1 2 8
15
5 1 2 3 4 5



Output:
1
415
13624

Author: calc_saransh
Date Added: 31-08-2011
Time Limit: 7 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TCL, TEXT, WSPC


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