# Awesome java solution

• First, we need a help function to do something:

``````    private int findKthNumber(long p, long q, long n) {
int result = 0;
while (p <= n) {
result += Math.min(q, n + 1) - p;
p *= 10;
q *= 10;
}
return result;
}
``````

The use of the upper function is to get the number of numbers in range `[p,min(q,n+1))` in lexicographical order. Because the number must be `<=n`, so it must `<n+1`.
Now, given a lower bound `p(inclusive)`, a upper bound `q(exclusive)`, and with a constraint `n(inclusive)`, we can easily find the number of numbers which are in range `[p,min(q,n+1))` in `lexicographical order` by using the upper function.
Moreover, we use long to avoid overflow, as `10*q, 10*q, n+1` may be greater than `Integer.MAX_VALUE`, of course, n is not necessary, but if n is `Integer.MAX_VALUE`(not in this problem), may cause overflow.
Next, comes the main function:

``````    public int findKthNumber(int n, int k) {
int result = 1;
while (k > 1) {
int count = findKthNumber(result, result + 1, n);
if (count < k) {
result++;
k -= count;
} else {
result *= 10;
k--;
}
}
return result;
}
``````

if k>count, we scan from left to right by increase result
if k<=count, we scan from up to bottom by multiply result by 10
very easy to understand, hope helps

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