A message signal with bandwidth $10 \; \mathrm{kHz}$ is Lower-Side Band SSB modulated with carrier frequency $f_{c 1}=10^{6} \mathrm{~Hz}$. The resulting signal is then passed through a Narrow-Band Frequency Modulator with carrier frequency $f_{c_{2}}=10^{9} \; \mathrm{Hz}$. The bandwidth of the output would be
- $4 \times 10^{4} \mathrm{~Hz}$
- $2 \times 10^{6} \mathrm{~Hz}$
- $2 \times 10^{9} \mathrm{~Hz}$
- $2 \times 10^{10} \mathrm{~Hz}$