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    Hint :

    1- Factorize M . (( M = p1 * p2 * p3 * ... * pr ))

    2 - Using Lucas theorem, compute NcR ( mod p_i ) .

    3 - Now you have r congruent equations. Each in form x = a_i ( mod n_i )

    4- Using CRT, solve them and find x. Actually x is NcR ( mod p1*p2*p3* ... * pr ) .