Problem D: Hartals

A social research organization has determined a simple set of parameters to simulate the behavior of the political parties of our country. One of the parameters is a positive integerh (called thehartal parameter) that denotes the average number of daysbetween two successivehartals (strikes) called by the correspondingparty. Though the parameter is far too simple to be flawless, it can still beused to forecast the damages caused byhartals. The following examplewill give you a clear idea:

Consider three political parties. Assume h₁ = 3,h₂ = 4 andh₃ = 8 where h_i is the hartal parameter for partyi(i = 1, 2, 3). Now, we will simulate the behavior of these three partiesforN = 14 days. One must always start the simulation on a Sunday and assumethat there will be nohartals on weekly holidays (on Fridays andSaturdays).

	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Days
	Su	Mo	Tu	We	Th	Fr	Sa	Su	Mo	Tu	We	Th	Fr	Sa
Party 1			x			x			x			x
Party 2				x				x				x
Party 3								x
Hartals			1	2				3	4			5

The simulation above shows that there will be exactly 5 hartals (on days3, 4, 8, 9 and 12) in 14 days. There will be nohartal on day 6 since itis a Friday. Hence we lose 5 working days in 2 weeks.

In this problem, giventhe hartal parameters for several political parties and the value ofN, yourjob is to determine the number of working days we lose in those N days.

Input

The first line of the input consists of a single integer T giving the numberof test cases to follow.

The first line of each test case contains an integerN ( $7 \le N \le 3650$ )giving the number of days over which the simulationmust be run. The next line contains another integer P ( $1 \le P \le 100$ )representing the number of political parties in this case. The i-th of thenext P lines contains a positive integer h_i (which will never be amultiple of 7) giving thehartal parameter for party i ( $1 \le i \leP$ ).