| ## Page 1 | |
| 10050 | |
| 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 integer h (called the hartal | |
| parameter) that denotes the average number of days between two successive hartals (strikes) called by | |
| the corresponding party. Though the parameter is far too simple to be flawless, it can still be used to | |
| forecast the damages caused by hartals. The following example will give you a clear idea: | |
| Consider three political parties. Assume h1 = 3, h2 = 4 and h3 = 8 where hi is the hartal parameter | |
| for party i (i = 1, 2, 3). Now, we will simulate the behavior of these three parties for N = 14 days. | |
| One must always start the simulation on a Sunday and assume that there will be no hartals on weekly | |
| holidays (on Fridays and Saturdays). | |
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| Days | |
| Su | |
| Mo | |
| Tu | |
| We | |
| Th | |
| Fr | |
| Sa | |
| Su | |
| Mo | |
| Tu | |
| We | |
| Th | |
| Fr | |
| Sa | |
| Party 1 | |
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| Party 2 | |
| x | |
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| Party 3 | |
| x | |
| Hartals | |
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| 5 | |
| The simulation above shows that there will be exactly 5 hartals (on days 3, 4, 8, 9 and 12) in 14 | |
| days. There will be no hartal on day 6 since it is a Friday. Hence we lose 5 working days in 2 weeks. | |
| In this problem, given the hartal parameters for several political parties and the value of N, your | |
| job 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 number of test cases to follow. | |
| The first line of each test case contains an integer N (7 ≤N ≤3650) giving the number of days over | |
| which the simulation must be run. The next line contains another integer P (1 ≤P ≤100) representing | |
| the number of political parties in this case. The i th of the next P lines contains a positive integer hi | |
| (which will never be a multiple of 7) giving the hartal parameter for party i (1 ≤i ≤P). | |
| Output | |
| For each test case in the input output the number of working days we lose. Each output must be on a | |
| separate line. | |
| Sample Input | |
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| 14 | |
| 3 | |
| 3 | |
| 4 | |
| 8 | |
| 100 | |
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| ## Page 2 | |
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| Sample Output | |
| 5 | |
| 15 |