A number system with moduli is de?ned by a vector of k moduli, [m1,m2, ···,mk].
The moduli must be pairwise co-prime, which means that, for any pair of moduli, the only common factor is 1.
In such a system each number n is represented by a string "-x1--x2-- ... --xk-" of its residues, one for each modulus. The product m1 ... mk must be greater than the given number n which is to be converted in the moduli number system.
For example, if we use the system [2, 3, 5] the number n = 11 is represented by "-1--2--1-",
the number n = 23 by "-1--2--3-". If we use the system [8, 7, 5, 3] the number n = 187 becomes "-3--5--2--1-".
You will be given a number n (n >= 0) and a system S = [m1,m2, ···,mk] and you will return a string "-x1--x2-- ...--xk-" representing the number n in the system S.
If the moduli are not pairwise co-prime or if the product m1 ... mk is not greater than n, return "Not applicable".
Examples:
fromNb2Str(11 [2,3,5]) -> "-1--2--1-"
fromNb2Str(6, [2, 3, 4]) -> "Not applicable", since 2 and 4 are not coprime
fromNb2Str(7, [2, 3]) -> "Not applicable" since 2 * 3 < 7
fromNb2Str 187 [8,7,5,3] -> "-3--5--2--1-"
fromNb2Str 6 [2, 3, 4] -> "Not applicable", since 2 and 4 are not coprime
fromNb2Str 7 [2, 3] -> "Not applicable", since 2 * 3 < 7