Sasha and Kolya decided to get drunk with Coke, again. This time they have *k* types of Coke. *i*-th type is characterised by its carbon dioxide concentration <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7223e2da7cf0d001a3a06ab38023d8f967968d61.png" style="max-width: 100.0%;max-height: 100.0%;"/>. Today, on the party in honour of Sergiy of Vancouver they decided to prepare a glass of Coke with carbon dioxide concentration <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3f84b61691275b2806285c0208e93684ddff5912.png" style="max-width: 100.0%;max-height: 100.0%;"/>. The drink should also be tasty, so the glass can contain only integer number of liters of each Coke type (some types can be not presented in the glass). Also, they want to minimize the total volume of Coke in the glass.

Carbon dioxide concentration is defined as the volume of carbone dioxide in the Coke divided by the total volume of Coke. When you mix two Cokes, the volume of carbon dioxide sums up, and the total volume of Coke sums up as well.

Help them, find the minimal natural number of liters needed to create a glass with carbon dioxide concentration <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3f84b61691275b2806285c0208e93684ddff5912.png" style="max-width: 100.0%;max-height: 100.0%;"/>. Assume that the friends have unlimited amount of each Coke type.
The first line contains two integers *n*, *k* (0 ≤ *n* ≤ 1000, 1 ≤ *k* ≤ 10<sup class="upper-index">6</sup>) — carbon dioxide concentration the friends want and the number of Coke types.

The second line contains *k* integers *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*k*</sub> (0 ≤ *a*<sub class="lower-index">*i*</sub> ≤ 1000) — carbon dioxide concentration of each type of Coke. Some Coke types can have same concentration.
In the first sample case, we can achieve concentration <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/bed0f5c3640139492194728ccc3ac55accf16a8e.png" style="max-width: 100.0%;max-height: 100.0%;"/> using one liter of Coke of types <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/9b37ab6b0795f08ffcc699d9101a9efb89374478.png" style="max-width: 100.0%;max-height: 100.0%;"/> and <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/d82574f3d78c4bd9d8ab9bda103e05a51e1b3161.png" style="max-width: 100.0%;max-height: 100.0%;"/>: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b23f59a536403f9a2364e971aa0bfc9a3411b366.png" style="max-width: 100.0%;max-height: 100.0%;"/>.

In the second case, we can achieve concentration <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/46aa9afb7ee4d932ca2c3f0d6535a9955fc8f0a8.png" style="max-width: 100.0%;max-height: 100.0%;"/> using two liters of <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/69b8967d23533c2caada3910f564294509450a59.png" style="max-width: 100.0%;max-height: 100.0%;"/> type and one liter of <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/abf5cbf9e8a81a0eff83ff53574dcabb097df44e.png" style="max-width: 100.0%;max-height: 100.0%;"/> type: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/4d2331fc733efc58d37745ff9a495a116ebd7e8a.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
400 4
100 300 450 500
2
50 2
100 25
3
500 3
1000 5 5
199
500 1
1000
-1
874 3
873 974 875
2
999 2
1 1000
999
326 18
684 49 373 57 747 132 441 385 640 575 567 665 323 515 527 656 232 701
3
314 15
160 769 201 691 358 724 248 47 420 432 667 601 596 370 469
4
0 1
0
1
0 1
1000
-1
345 5
497 135 21 199 873
5
641 8
807 1000 98 794 536 845 407 331
7
852 10
668 1000 1000 1000 1000 1000 1000 639 213 1000
10
710 7
854 734 63 921 921 187 978
5
134 6
505 10 1 363 344 162
4
951 15
706 1000 987 974 974 706 792 792 974 1000 1000 987 974 953 953
6
834 10
921 995 1000 285 1000 166 1000 999 991 983
10
917 21
999 998 1000 997 1000 998 78 991 964 985 987 78 985 999 83 987 1000 999 999 78 83
12
971 15
692 1000 1000 997 1000 691 996 691 1000 1000 1000 692 1000 997 1000
11
971 108
706 706 991 706 988 997 996 997 991 996 706 706 996 706 996 984 1000 991 996 1000 724 724 997 991 997 984 997 1000 984 996 996 997 724 997 997 1000 997 724 984 997 996 988 997 706 706 997 1000 991 706 988 997 724 988 706 996 706 724 997 988 996 991 1000 1000 724 988 996 1000 988 984 996 991 724 706 988 991 724 1000 1000 991 984 984 706 724 706 988 724 984 984 991 988 991 706 997 984 984 1000 706 724 988 984 996 1000 988 997 984 724 991 991
10
1000 16
536 107 113 397 613 1 535 652 730 137 239 538 764 431 613 273
-1
998 2
1 1000
999
998 3
1 999 1000
500
998 4
1 2 999 1000
499
500 2
1000 2
499
508 15
0 998 997 1 1 2 997 1 997 1000 0 3 3 2 4
53
492 2
706 4
351
672 5
4 6 1000 995 997
46
410 4
998 8 990 990
54
499 2
1000 2
998
995 5
996 997 998 999 1000
-1
500 3
499 1000 300
7
499 2
0 1000
1000
1000 10
0 1 2 3 4 5 6 7 8 9
-1
501 2
1 1000
999
print("_RANDOM_GUESS_1689419884.7016466")# 1689419884.7016664