```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cub/cub.cuh>
#include <cuda_runtime.h>
#include <algorithm>

constexpr int THREADS = 256;
constexpr int ITEMS = 8;
constexpr int TILE = THREADS * ITEMS;

struct RunningPrefix {
    float total;

    __device__ RunningPrefix() : total(0.0f) {}

    __device__ float operator()(float aggregate) {
        float previous = total;
        total += aggregate;
        return previous;
    }
};

__global__ void scan_rows(
    const float* __restrict__ x,
    float* __restrict__ y,
    int64_t rows,
    int64_t columns
) {
    using Load = cub::BlockLoad<
        float, THREADS, ITEMS, cub::BLOCK_LOAD_WARP_TRANSPOSE>;
    using Scan = cub::BlockScan<
        float, THREADS, cub::BLOCK_SCAN_WARP_SCANS>;
    using Store = cub::BlockStore<
        float, THREADS, ITEMS, cub::BLOCK_STORE_WARP_TRANSPOSE>;

    __shared__ union {
        typename Load::TempStorage load;
        typename Scan::TempStorage scan;
        typename Store::TempStorage store;
    } storage;

    for (int64_t row = blockIdx.x; row < rows; row += gridDim.x) {
        const float* input = x + row * columns;
        float* output = y + row * (columns + 1);

        if (threadIdx.x == 0) {
            output[0] = 0.0f;
        }

        RunningPrefix prefix;
        for (int64_t offset = 0; offset < columns; offset += TILE) {
            const int valid = static_cast<int>(
                columns - offset < TILE ? columns - offset : TILE);
            float values[ITEMS];

            Load(storage.load).Load(input + offset, values, valid, 0.0f);
            __syncthreads();

            Scan(storage.scan).InclusiveSum(values, values, prefix);
            __syncthreads();

            Store(storage.store).Store(output + offset + 1, values, valid);
            __syncthreads();
        }
    }
}

torch::Tensor exclusive_scan_rows(torch::Tensor x) {
    TORCH_CHECK(x.is_cuda(), "Expected a CUDA tensor");
    TORCH_CHECK(x.scalar_type() == at::kFloat, "Expected float32");
    TORCH_CHECK(x.dim() == 2 && x.is_contiguous(),
                "Expected a contiguous matrix");
    TORCH_CHECK(x.size(1) > 0, "Scan dimension must be nonempty");

    const c10::cuda::CUDAGuard guard(x.device());

    // The original [:-1] slices dimension zero, removing the final row.
    const int64_t rows = std::max<int64_t>(x.size(0) - 1, 0);
    const int64_t columns = x.size(1);
    auto output = torch::empty({rows, columns + 1}, x.options());

    if (rows != 0) {
        const int blocks = static_cast<int>(
            std::min<int64_t>(rows, 65535));
        scan_rows<<<blocks, THREADS, 0,
                    at::cuda::getCurrentCUDAStream()>>>(
            x.data_ptr<float>(),
            output.data_ptr<float>(),
            rows,
            columns);
        C10_CUDA_KERNEL_LAUNCH_CHECK();
    }

    return output;
}
"""

_extension = load_inline(
    name="exclusive_cumsum_rows_cuda_v1",
    cpp_sources="torch::Tensor exclusive_scan_rows(torch::Tensor x);",
    cuda_sources=_cuda_source,
    functions=["exclusive_scan_rows"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, dim):
        super().__init__()
        self.dim = dim

    def forward(self, x):
        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.ndim == 2
            and self.dim in (1, -1)
            and x.size(1) > 0
        ):
            return _extension.exclusive_scan_rows(x.contiguous())

        exclusive_cumsum = torch.cat(
            (
                torch.zeros_like(
                    x.select(self.dim, 0).unsqueeze(self.dim)
                ),
                x,
            ),
            dim=self.dim,
        )[:-1]
        return torch.cumsum(exclusive_cumsum, dim=self.dim)
```