Pandas DataFrame - Fill NaNs of columns based on values of other columns

I have a wide data frame with several years:

df = pd.DataFrame(index=pd.Index([29925, 223725, 280165, 813285, 956765], name='ID'),                  columns=pd.Index([1991, 1992, 1993, 1994, 1995, 1996, '2010-2012'], name='Year'),                  data = np.array([[np.NaN, np.NaN, 16, 17, 18, 19, np.NaN],                                   [16, 17, 18, 19, 20, 21, np.NaN],                                   [np.NaN, np.NaN, np.NaN, np.NaN, 16, 17, 31],                                   [np.NaN, 22, 23, 24, np.NaN, 26, np.NaN],                                   [36, 36, 37, 38, 39, 40, 55]]))Year     1991  1992  1993  1994  1995  1996  2010-2012ID                                                    29925     NaN   NaN  16.0  17.0  18.0  19.0        NaN223725   16.0  17.0  18.0  19.0  20.0  21.0        NaN280165    NaN   NaN   NaN   NaN  16.0  17.0       31.0813285    NaN  22.0  23.0  24.0   NaN  26.0        NaN956765   36.0  36.0  37.0  38.0  39.0  40.0       55.0

The values in each row are the age of each person, with each holding a unique ID. I want to fill the NaN of this data frame in each year of every row, based on the existing age values in each row.

For example, ID 29925 is 16 in 1993, we know they are 15 in 1992 and 14 in 1991, therefore we want to replace the NaN for 29925 in the columns 1992 and 1991. Similarly, I want to replace the NaN in the column2010-2012 based on the existing age values for 29925. Let's assume that 29925 is 15 years older from 1996 in the 2010-2012 column. What is the fastest way to do this for the whole data frame - i.e for all IDs?