diff --git a/Project.toml b/Project.toml
index 7e62251..c80c9f0 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "MCIntegration"
 uuid = "ea1e2de9-7db7-4b42-91ee-0cd1bf6df167"
 authors = ["Kun Chen", "Xiansheng Cai", "Pengcheng Hou"]
-version = "0.4.0"
+version = "0.4.1"
 
 [deps]
 Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
diff --git a/example/benchmark/cuba/benchmark.jl b/example/benchmark/cuba/benchmark.jl
index b4cfd8d..6131836 100644
--- a/example/benchmark/cuba/benchmark.jl
+++ b/example/benchmark/cuba/benchmark.jl
@@ -72,6 +72,20 @@ function test2(x, c)
     t11(x[1], x[2], x[3])
 end
 
+@inbounds function test3(x, f, c)
+    @inbounds f[1] = t1(x[1], x[2], x[3])
+    @inbounds f[2] = t2(x[1], x[2], x[3])
+    @inbounds f[3] = t3(x[1], x[2], x[3])
+    @inbounds f[4] = t4(x[1], x[2], x[3])
+    @inbounds f[5] = t5(x[1], x[2], x[3])
+    @inbounds f[6] = t6(x[1], x[2], x[3])
+    @inbounds f[7] = t7(x[1], x[2], x[3])
+    @inbounds f[8] = t8(x[1], x[2], x[3])
+    @inbounds f[9] = t9(x[1], x[2], x[3])
+    @inbounds f[10] = t10(x[1], x[2], x[3])
+    @inbounds f[11] = t11(x[1], x[2], x[3])
+end
+
 @info "Performance of Cuba.jl:"
 for alg in (vegas, suave, divonne, cuhre)
     # Run the integrator a first time to compile the function.
@@ -120,9 +134,9 @@ end
 @info "Performance of MCIntegration:"
 for alg in (:vegas, :vegasmc)
     # Run the integrator a first time to compile the function.
-    integrate(test2; dof=[[3,] for i in 1:11], neval=1e4, solver=alg, print=-1)
+    integrate(test3; dof=[[3,] for i in 1:11], neval=1e4, solver=alg, print=-1, inplace=true)
     start_time = time_ns()
-    integrate(test2; dof=[[3,] for i in 1:11], neval=1e5, solver=alg, print=-2)
+    integrate(test3; dof=[[3,] for i in 1:11], neval=1e5, solver=alg, print=-2, inplace=true)
     # Cuba will run for 1e6 steps
     end_time = time_ns()
     println(@sprintf("%10.6f", Int(end_time - start_time) / 1e9),
@@ -146,7 +160,7 @@ end
 
 cd(@__DIR__) do
     if mtime("benchmark.c") > mtime("benchmark-c")
-        run(`gcc -O3 -I $(Cuba.Cuba_jll.artifact_dir)/include -o benchmark-c benchmark.c $(Cuba.Cuba_jll.libcuba_path) -lm`)
+        run(`gcc -O1 -I $(Cuba.Cuba_jll.artifact_dir)/include -o benchmark-c benchmark.c $(Cuba.Cuba_jll.libcuba_path) -lm`)
     end
     @info "Performance of Cuba Library in C:"
     withenv(Cuba.Cuba_jll.JLLWrappers.LIBPATH_env => Cuba.Cuba_jll.LIBPATH[]) do
@@ -155,7 +169,7 @@ cd(@__DIR__) do
 
     if success(`which gfortran`)
         if mtime("benchmark.f") > mtime("benchmark-fortran")
-            run(`gfortran -O3 -fcheck=no-bounds -cpp -o benchmark-fortran benchmark.f $(Cuba.Cuba_jll.libcuba_path) -lm`)
+            run(`gfortran -O1 -fcheck=no-bounds -cpp -o benchmark-fortran benchmark.f $(Cuba.Cuba_jll.libcuba_path) -lm`)
         end
         @info "Performance of Cuba Library in Fortran:"
         withenv(Cuba.Cuba_jll.JLLWrappers.LIBPATH_env => Cuba.Cuba_jll.LIBPATH[]) do
diff --git a/src/distribution/variable.jl b/src/distribution/variable.jl
index dff7680..315961b 100644
--- a/src/distribution/variable.jl
+++ b/src/distribution/variable.jl
@@ -639,6 +639,22 @@ function padding_probability(config, idx)
     end
     return prob
 end
+function padding_probability!(config, probs::AbstractVector)
+    for i in eachindex(probs)
+        probs[i] = 1.0
+        dof = config.dof[i]
+        for (vi, var) in enumerate(config.var)
+            offset = var.offset
+            for pos = dof[vi]+1:config.maxdof[vi]
+                probs[i] *= var.prob[pos+offset]
+            end
+        end
+        if probs[i] < TINY
+            @warn "probability is either too small or negative : $(probs[i])"
+        end
+        # @assert probs[i] ≈ padding_probability(config, i) "$(probs[i]) vs $(padding_probability(config, i))"
+    end
+end
 
 function delta_probability(config, curr=config.curr; new)
     prob = 1.0
diff --git a/src/vegas/montecarlo.jl b/src/vegas/montecarlo.jl
index 9bfeea2..506942b 100644
--- a/src/vegas/montecarlo.jl
+++ b/src/vegas/montecarlo.jl
@@ -78,6 +78,8 @@ function montecarlo(config::Configuration{Ni,V,P,O,T}, integrand::Function, neva
 
     relativeWeights = zeros(T, Ni)
     weights = zeros(T, Ni)
+    padding_probability = ones(Ni)
+    diff = [config.dof[i] == config.maxdof for i in 1:Ni] # check if the dof is the same as the maxdof, if the same, then there is no need to update the padding probability
 
     ################## test integrand type stability ######################
     if debug
@@ -127,6 +129,12 @@ function montecarlo(config::Configuration{Ni,V,P,O,T}, integrand::Function, neva
                 # jac *= Dist.create!(var, idx + var.offset, config)
             end
         end
+        # Dist.padding_probability!(config, padding_probability)
+        for i in 1:Ni
+            if diff[i] == false
+                padding_probability[i] = Dist.padding_probability(config, i)
+            end
+        end
         # weights = @_expanded_integrand(config, integrand, 1) # very fast, but requires explicit N
         # weights = integrand_wrap(config, integrand) #make a lot of allocations
         if inplace
@@ -140,15 +148,18 @@ function montecarlo(config::Configuration{Ni,V,P,O,T}, integrand::Function, neva
             @assert typeof(weights) <: Tuple || typeof(weights) <: AbstractVector "the integrand should return a vector with $(Ni) elements, but it returns a vector elements! $(typeof(weights)))"
         end
 
+        # println("before: ", weights, "with jac = ", jac)
+
         if (ne % measurefreq == 0)
             if isnothing(measure)
+                # println("after: ", weights * jac)
                 for i in 1:Ni
-                    config.observable[i] += weights[i] * jac
+                    config.observable[i] += weights[i] * padding_probability[i] * jac
                 end
                 # observable += weights * jac
             else
                 for i in 1:Ni
-                    relativeWeights[i] = weights[i] * jac
+                    relativeWeights[i] = weights[i] * padding_probability[i] * jac
                 end
                 (fieldcount(V) == 1) ?
                 measure(config.var[1], config.observable, relativeWeights, config) :
@@ -166,6 +177,7 @@ function montecarlo(config::Configuration{Ni,V,P,O,T}, integrand::Function, neva
             for idx in eachindex(weights)
                 w2 = abs(weights[idx])
                 j2 = jac
+                # ! warning: need to check whether to use jac or jac*padding_probability[idx]
                 if debug && (isfinite(w2) == false)
                     @warn("abs of the integrand $idx = $(w2) is not finite at step $(config.neval)")
                 end
diff --git a/src/vegas_mc/updates.jl b/src/vegas_mc/updates.jl
index 3d46656..b1eb15c 100644
--- a/src/vegas_mc/updates.jl
+++ b/src/vegas_mc/updates.jl
@@ -79,6 +79,7 @@ function changeVariable(config::Configuration{N,V,P,O,T}, integrand, inplace,
     for i in 1:N+1
         _padding_probability[i] = Dist.padding_probability(config, i)
     end
+    # Dist.padding_probability!(config, _padding_probability)
     # println(_padding_probability)
     newProbability = config.reweight[config.norm] * _padding_probability[config.norm] #normalization integral
     for i in 1:N #other integrals
diff --git a/test/montecarlo.jl b/test/montecarlo.jl
index 26fff19..ed44632 100644
--- a/test/montecarlo.jl
+++ b/test/montecarlo.jl
@@ -197,6 +197,24 @@ function TestComplex2_inplace(totalstep, alg)
     return res
 end
 
+function TestHyperSphere(totalstep, alg, N)
+    function volume_inverse(d)
+        euler = 2.71828182845904523536028747135266249775724709369995957496696763
+        return (d / (2π * euler))^(d / 2) * sqrt(d) * sqrt(π)
+    end
+
+    function f(x, w, c)
+        _w = x[1]^2
+        for i = 1:c.userdata
+            _w += x[i+1]^2
+            w[i] = _w < 1.0 ? volume_inverse(i + 1) : 0.0
+        end
+    end
+
+    res = integrate(f; var=Continuous(-1, 1), dof=[[i + 1,] for i in 1:N], userdata=N, neval=totalstep, print=-1, solver=alg, debug=false, inplace=true)
+    return res
+end
+
 # struct Weight <: AbstractVector
 #     d::Tuple{Float64,Float64}
 #     function Weight(a, b)
@@ -311,6 +329,9 @@ end
     println("inplace Complex2")
     check_complex(TestComplex2_inplace(neval, :vegas), [0.5, 1.0 / 3 * 1im])
 
+    println("hypersphere")
+    check(TestHyperSphere(neval, :vegas, 3), [0.9230, 0.94724, 0.96118])
+
     # println("vector type")
     # check_vector(Test_user_type(neval, :vegas), [0.5, 1.0 / 3])
 end
@@ -358,6 +379,9 @@ end
     println("inplace Complex2")
     check_complex(TestComplex2_inplace(neval, :vegasmc), [0.5, 1.0 / 3 * 1im])
 
+    println("hypersphere")
+    check(TestHyperSphere(neval, :vegasmc, 3), [0.9230, 0.94724, 0.96118])
+
     # println("vector type")
     # check_vector(Test_user_type(neval, :vegamcs), [0.5, 1.0 / 3])
 end