If ${ }^{404}{C}_4-{}^4{C}_1.{}^{303}{C}_4+{}^4{C}_2.{}^{202}{C}_4-{}^4{C}_3.{}^{101}{C}_4=k^4$ then the value of $k$ is

The coefficient of $x^4$ in $4c_o{\left(1+x\right)}^{404}-4c_1{\left(1+x\right)}^{303}+4c_2{\left(1+x\right)}^{202}-4c_3{\left(1+x\right)}^{101}+4c_4$ in ${\left[{\left(1+x\right)}^{101}-1\right]}^4={\left[101c_{1}x+101c_2{x}^2+\mathrm{.....}+101c_{101}{x}^{101}\right]}^4$ is ${\left(101\right)}^4$