Given n strings S1,S2,...,Sn. There are q queries, each consisting of two integers x,y. Check whether Sx is a substring (not necessarily contiguous) of Sy or if Sy is a substring (not necessarily contiguous) of Sx.
### Input
- The first line contains two integers n,q.
- The next n lines, where the i-th line represents the string Si.
- The next q lines, each containing two integers x,y.
### Output
- For each query, print YES if Sx is a substring of Sy or if Sy is a substring of Sx, otherwise print NO.
### Constraints
- 1≤n,q≤105.
- 1≤∑|Si|≤106
- 1≤x,y≤n.
- All strings consist only of lowercase letters.
### Example
Input:
33aabdbdacb212313
Output:
NOYESNO
