It's Lunar New Year, and $$$n$$$ ($$$1 \leq n \leq 100$$$) lion dancers are performing a traditional lion dance through a grid-like corridor. The corridor is divided into $$$m$$$ ($$$1 \leq m \leq 10^5$$$) sections, arranged as columns of platforms. Each section $$$i$$$ consists of $$$k_i$$$ platforms ($$$n \leq k_i \leq 10^5$$$) stacked vertically in a grid-like structure. Each platform can hold exactly one dancer, and no two dancers can share the same platform at any time.

The dancers start their performance in the first column and must move through the grid from left to right. At each step, all $$$n$$$ dancers move as a team to the next column, each landing on one of the available platforms in the new section. This process continues until they reach the final column.

Additionally, the lion dancers are numbered from $$$1$$$ to $$$n$$$, with dancer $$$1$$$ always performing on the lowest platform and dancer $$$n$$$ on the highest platform in any column. This order must be maintained throughout the performance: if dancer A is below dancer B in one column, then dancer A must be below dancer B in every other column.

Your task is to determine the number of distinct ways the lion dancers can perform their routine, moving from the first column to the last. Two routines are considered distinct if, at any step, at least one dancer occupies a different platform compared to the other routine. Please output the answer mod $$$10^9+7$$$.