Merge two trees into a rectangular matrix in Mathematica

Question

How can I merge two trees, t and s, so as to form a square matrix below, where both trees starts from top-left (as shown), and occupy lower and upper triangular forms (in a transpose fashion). Trees can get larger. Diagonal contains zeros, but I will store some other information there later. Up to transpose, it doesn't matter which tree is on the bottom.

t = {{1}, {1, 2}, {1, 2, 3}, {1, 2, 3, 4}}
s = 10 t

output

{{0, 10, 10, 10, 10}, {1, 0, 20, 20, 20}, {1, 2, 0, 30, 30}, {1, 2, 3, 0, 40}, {1, 2, 3, 4, 0}}

or in matrix form:

Answer 1

Transpose[#[[1]]] + #[[2]] &[PadRight[{s, t}, {2, -5, 5}]]

Answer 2

t = {{1}, {1, 2}, {1, 2, 3}, {1, 2, 3, 4}}
tm = Prepend[t, {}];
a = PadRight[#, 5] & /@ tm
a + 10 Transpose[a] // MatrixForm

UPDATE

Exploiting the much better and more concise advice in comment by ybeltukov:

b = ArrayPad[PadRight@t, {{1, 0}, {0, 1}}]
b + 10 Transpose[b] // MatrixForm