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# 1545. Find Kth Bit in Nth Binary String | ||
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Given two positive integers n and k, the binary string Sn is formed as follows: | ||
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S1 = "0" | ||
Si = Si - 1 + "1" + reverse(invert(Si - 1)) for i > 1 | ||
Where + denotes the concatenation operation, reverse(x) returns the reversed string x, and invert(x) inverts all the bits in x (0 changes to 1 and 1 changes to 0). | ||
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For example, the first four strings in the above sequence are: | ||
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S1 = "0" | ||
S2 = "011" | ||
S3 = "0111001" | ||
S4 = "011100110110001" | ||
Return the kth bit in Sn. It is guaranteed that k is valid for the given n. | ||
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### Example 1: | ||
``` | ||
Input: n = 3, k = 1 | ||
Output: "0" | ||
Explanation: S3 is "0111001". | ||
The 1st bit is "0". | ||
``` | ||
### Example 2: | ||
``` | ||
Input: n = 4, k = 11 | ||
Output: "1" | ||
Explanation: S4 is "011100110110001". | ||
The 11th bit is "1". | ||
``` | ||
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### Constraints: | ||
``` | ||
1 <= n <= 20 | ||
1 <= k <= 2n - 1 | ||
``` |