Grandmother's Wage in Today's Money

In 1990 Grandmother earned 1200 crowns a month; her grandson earns 2600 in 2020. Who earned more? Only a price index can say, because a crown bought more in 1990.

index maps calendar years to the value of a price index (any base: the year that reads 100, if any, does not matter). An amount a in year s is worth, in the money of year y,

and rebasing the index to year y means dividing every value by \text{index}_y and multiplying by 100, so year y reads 100 and every ratio between years stays the same.

Write real_wages(index, wages, base_year) where wages maps some years to a nominal wage. Return a pair of dicts (rebased, real):

• rebased: every year of index, mapped to its rebased value with base_year at 100;
• real: every year of wages, mapped to that wage expressed in base_year's money.

Examples

Input:  index = {1990: 62.0, 2000: 80.6, 2010: 100.0, 2020: 124.0}
        wages = {1990: 1200, 2020: 2600}, base_year = 2020
Output: ({1990: 50.0, 2000: 65.0, 2010: 80.64516129032258, 2020: 100.0},
         {1990: 2400.0, 2020: 2600.0})
Explanation: prices doubled from 1990 (62) to 2020 (124), so 1200 crowns of 1990 buy
what 2400 crowns bought in 2020. The grandson's wage is higher in real terms too.

Input:  the same index and wages, base_year = 1990
Output: ({1990: 100.0, 2000: 130.0, 2010: 161.29032258064515, 2020: 200.0},
         {1990: 1200.0, 2020: 1300.0})

Constraints

• base_year and every year of wages are years of index
• floats are compared with a tolerance of 1e-6

Goals

• Rebase a price index so that a chosen year reads 100
• Convert an amount of money from one year into another year's money
• Compare wages from different years in the same money