A rich old man had \( k \) sons and \( N \) camels in the herd. The will of the father stated that his \( r \)-th son should receive \( 1/ N_r\) of his camels for \( r = 1, 2, \dots, k\). Since \( N+1 \) is a common multiple of \( N_1, N_2, \dots, N_k \), the sons could not divided \( N \) camels as their father wished. The sons visited a wise man to solve the issue. The wise man listened about the will, and he brought his own camel, which he added to the herd. The herd was then divided up according to the old man’s wishes. The wise man then took back the one camel that remained, which was his own. For given \( k \), find the maximal number of camels \( N \equiv N(k) \) for which there is a solution to the problem where \( N_1, N_2, \dots, N_k\) are positive integers.