Comparing two numbers written in index form like 2^11 and 3^7 is not difficult, as any calculator would confirm that 2^11 = 2048 < 3^7 = 2187. However, confirming that 632382^518061 > 519432^525806 would be much more difficult, as both numbers contain over three million digits.

Create a function that takes Base-Exponent pairs and returns the line number which has the greatest numerical value.

Examples

largest_exponential([
  (519432,525806),
  (632382,518061),
  (78864,613712),
  (466580,530130),
  (780495,510032)
]) ➞ 5

largest_exponential([
  (375856,539061),
  (768907,510590),
  (165993,575715),
  (976327,501755),
  (898500,504795),
  (360404,540830)
]) ➞ 4

largest_exponential([
  (478714,529095),
  (694144,514472)
]) ➞ 1

Notes

As mentioned, the actual values may contain some millions of digits. So, it's impractical to actually calculate the values and compare them.