Given below are two statements:
Statement $I$: For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.
Statement $II$: For all elements, nuclei with less binding energy per nucleon transform to nuclei with greater binding energy per nucleon.
In the light of the above statements, choose the correct answer from the options given below:

• A
  Both Statement $I$ and Statement $II$ are true
• B
  Statement $I$ is true but Statement $II$ is false
• C
  Both Statement $I$ and Statement $II$ are false
• D
  Statement $I$ is false but Statement $II$ is true