How do I produce a BarLegend with the default coloring of a ContourPlot, using Legended?

Legended[ContourPlot[x y, {x, 0, 1}, {y, 0, 1}],
 Placed[BarLegend[{ColorData["M10DefaultDensityGradient"], {0, 1}}, 
   LegendLayout -> "Row"], Below]]

I found the name of the color scheme by evaluating

plot = ContourPlot[x y, {x, 0, 1}, {y, 0, 1}, PlotLegends -> Automatic]

and looking at the expression of the result. As Legended accepts two arguments with the second being the legend, this can be easily done by running

plot[[2]] // InputForm