P18577 [HackerEarth] Chintu is a final year computer engineering student , who loves programming . All the time he is busy coding . His friends though don't like to code and
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题目描述

Chintu is a final year computer engineering student , who loves programming . All the time he is busy coding . His friends though don't like to code and
always want to enjoy . They ask their friend Chintu to accompany them on their trip to Goa , but he refuses . They persuade him , so he agrees on one condition
, if they solve the following problem . He asks them to prepare a list of friends going to Goa maintaining the following property , for the first k+1 friends
the name of ith friend(indexing from 0) , where 0 ≤ i < k, should be a substring of the (i+1)th friend .
Find the number of permutations of all friends which are going on the Trip .
Since the friends are not that smart, they have asked you to solve it . Please help them .

Note:
Since the value can be very large take modulo : 10^9 + 9.
All names are lowercase.
All the friends names are distinct.

Input :
The first line contains T , the number of test cases .
The next line contains n , the total number of friends and k.
The next n lines contains the names of the friends.

Constraints :
1 ≤ T ≤ 100
3 ≤ n ≤30 , 0 ≤ k ≤ 29
Length of each name , L is 2 ≤ L ≤ 30.

output :
a single integer giving the number of permutations.

SAMPLE INPUT
2
3 1
raj
rajunder
raju
3 0
rajat
kashish
piyush

SAMPLE OUTPUT
3
6

Explanation

for the first test case , since k = 1 , we have to maintain the order for only the first and the second i.e. k+1 friends , so the
possible configurations are

raj rajunder raju
raj raju rajunder
raju rajunder raj
So, output 3

for the second case , since k = 0, therefore answer is 6 . i.e. all possible configurations.

输入格式

见题面

输出格式

见题面

样例输入
100 3 1 raj jurajnder uraj 3 1 raj rajunder raju 3 0 rajat kashish piyush 3 2 rajat kashish piyush 3 1 raj unrajnder uraj 3 3 yes yess yesss 20 2 hdikashta dsakashhei faffakashtaro fadjalkash fdjkashga akashma skashko kash piyushmittal shivamadlakha rajta raj rajma rajjiro rajsuke rajtaro gambhirraj rajhei rajichi shiv 30 2 hqghumeaylnlfd fircvscxggbwkfnq uxwfnfozvsrtkjpr pggxrpnrv stmwcysyycqpevikeffmzni kkasvwsrenzkycxfxtl gypsfad ooefxzbcoejuvpvabo gpoeylfpbnpljvrvipyamye wqnqrq mxuj loovaowuxwhmsncb coksfzkvatxd nly yh ixjswnkk fnuxxzrzbmnmgqooketly nkoaugzqrc diut iojwayyzpvscmpsajlf gu fa ovlzylntrkdcpwsrtesjwhdiz obzcnfwlqijtvdwvx rcbldvgylw busbmborxtlhcsm xo gmgnkeufdxotog gxpeyanfetcukepz hkljugggekj 30 1 hqghumeaylnlfd fadfhqghumeaylnlfdraj timehqghumeaylnlfd fircvscxggbwkfnq fadffircvscxggbwkfnqraj timefircvscxggbwkfnq uxwfnfozvsrtkjpr fadfuxwfnfozvsrtkjprraj timeuxwfnfozvsrtkjpr pggxrpnrv fadfpggxrpnrvraj timepggxrpnrv stmwcysyycqpevikeffmzni fadfstmwcysyycqpevikeffmzniraj 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blbbgwa blbbgwadbfzrwmohscfwygavzjaoxr blbbgwadbfzrwmo blbbgwadbfzrwmohs blbbgwadbfzrwm 30 22 huesblhlpxnpoym huesblhlpxnpoymjeebhd huesblhlpxnpoymjeebhdj hue huesblhlpxnpo huesblhlpxnpoymj huesblhlpxnpoymjeebhdjhtjqfjkh huesblhlpxnpoymjeebhdjh hu huesblhlpx huesblhlpxnpoymjeebhdjhtjq huesblhlpxnpoymjeebhdjhtjqfj huesbl huesblhlpxnpoymjeebhdjht huesblhlpxnpoymjee huesblhlpxn hues huesblhlpxnpoymjeeb huesblhlpxnpoy huesblh huesblhlpxnp h huesblhl huesblhlpxnpoymjeebhdjhtjqfjk huesblhlpxnpoymjeebhdjhtjqf huesblhlpxnpoymje huesb huesblhlp huesblhlpxnpoymjeebhdjhtj huesblhlpxnpoymjeebh 30 13 eqkohktevfnorjbe eqkohktevfnorjbezawpyz eqkohktevfnorjbezawpyzaud eqkohk eqkohktevfno eqkohktevfnorjbezawpyzaudwuxq eqkohkt eqkohktevfn e eqkohktevfnorjb eqkohktevfnorjbezawpyzaudwux eqkohktevfnorjbezawpyzaudwuxql eqkohktevfnor eqkohktevfnorjbeza eqkohktevfnorjbezawpyzaudwu eqkoh eqkohktev eqkohktevfnorjbezawpyzaudw eqkohktevfnorjbez eqkohktevfnorjbezawpy eq eqkohktevfnorjbezawpyza eqkohktevf eqk 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样例输出
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