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"""

Insertion:

insert_one_bit(num, bit, i): insert exact one bit at specific position

For example:

Input: num = 10101 (21)

insert_one_bit(num, 1, 2): 101101 (45)

insert_one_bit(num, 0, 2): 101001 (41)

insert_one_bit(num, 1, 5): 110101 (53)

insert_one_bit(num, 1, 0): 101011 (43)

insert_mult_bits(num, bits, len, i): insert multiple bits with len at specific position

For example:

Input: num = 101 (5)

insert_mult_bits(num, 7, 3, 1): 101111 (47)

insert_mult_bits(num, 7, 3, 0): 101111 (47)

insert_mult_bits(num, 7, 3, 3): 111101 (61)

"""

"""

Insert exact one bit at specific position

Algorithm:

1. Create a mask having bit from i to the most significant bit, and append the new bit at 0 position

2. Keep the bit from 0 position to i position ( like 000...001111)

3. Merge mask and num

"""

def insert_one_bit(num, bit, i):

# Create mask

mask = num >> i

mask = (mask << 1) | bit

mask = mask << i

# Keep the bit from 0 position to i position

right = ((1 << i) - 1) & num

return right | mask

def insert_mult_bits(num, bits, len, i):

mask = num >> i

mask = (mask << len) | bits

mask = mask << i

right = ((1 << i) - 1) & num

return right | mask