Append columns to DataFrame form another DataFrame

Question

everyone! Can you pleas help me with the bellow! I have the first df_1:

key	end
1	10
1	20
2	30
2	40

And the second df_2:

key	time
1	13
1	25
2	35
2	45

I need add columns from df_1 to df_2 with the condition: df_1['key'] == df_2['key'] and df_2['time'] > df_1['end']

The final solution should look like:

key	time	end_1	end_2
1	13	10
1	25	10	20
2	35	30
2	45	30	40

I was thinking to solve it like on the example bellow:

for index_1, row_1 in df_2.iterrows():
    for index_2, row_2 in df_1.iterrows():
        if row_1[0] == row_2[0] and row_1[1] > row_2[2]:
            row_1.append(row_2)

But it doesn't work

I would appreciate if someone could help me.