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from math import comb

def count_smooth_permutations(a, b, c, p):
    n = a + b - 1  
   
    
    num_permutations = (comb(n, a) * comb(n-1, b-1)) % p
    
    print(n, num_permutations)

count_smooth_permutations(2, 2, 3, 10000019)
count_smooth_permutations(2, 3, 3, 999999937)
count_smooth_permutations(8, 9, 11, 15872567)