In the presence of dry ether, formaldehyde $\left(\mathrm{A}\right)$ undergoes nucleophilic addition with Grignard reagent (obtained from methyl iodide and metallic magnesium) to give compound ${}^{\text{'}}\mathrm{B}^{\text{'}}$. The compound ${}^{\text{'}}\mathrm{B}^{\text{'}}$ on heating with diazomethane in the presence of fluoroboric acid gives compound ${}^{\text{'}}\mathrm{C}^{\text{'}}$. Identify compounds ${}^{\text{'}}\mathrm{B}^{\text{'}}$ and ${}^{\text{'}}\mathrm{C}^{\text{'}}$.