Consider a database table T containing two columns X and Y each of type integer. After the creation of the table, one record (X=1, Y=1) is inserted in the table. Let MX and MY denote the respective maximum values of X and Y among all records in the table at any point in time. Using MX and MY, new records are inserted in the table 128 times with X and Y values being MX+1, 2*MY+1 respectively. It may be noted that each time after the insertion, values of MX and MY change. What will be the output of the following SQL query after the steps mentioned above are carried out? SELECT Y FROM T WHERE X=7;

Initially, the table contains one row:

• Initial state: $(X_1, Y_1) = (1, 1)$, so $MX = 1$ and $MY = 1$.

In each subsequent insertion step $k$ (for $k = 1, 2, \dots, 128$):

• A new record is inserted with $X_{k+1} = MX + 1$ and $Y_{k+1} = 2 \times MY + 1$.

Tracing the values of $X$ and $Y$ inserted into the table:

• Step 1: $X_2 = 1 + 1 = 2$, $Y_2 = 2(1) + 1 = 3 = 2^2 - 1$

• Step 2: $X_3 = 2 + 1 = 3$, $Y_3 = 2(3) + 1 = 7 = 2^3 - 1$

• Step 3: $X_4 = 3 + 1 = 4$, $Y_4 = 2(7) + 1 = 15 = 2^4 - 1$

• Step 4: $X_5 = 4 + 1 = 5$, $Y_5 = 2(15) + 1 = 31 = 2^5 - 1$

• Step 5: $X_6 = 5 + 1 = 6$, $Y_6 = 2(31) + 1 = 63 = 2^6 - 1$

• Step 6: $X_7 = 6 + 1 = 7$, $Y_7 = 2(63) + 1 = 127 = 2^7 - 1$

In general, for a given $X = n$, the corresponding value of $Y$ is $2^n - 1$.

For $X = 7$:

Thus, the query SELECT Y FROM T WHERE X=7; returns 127 (Option A).